9 Area, Perimeter and Volume


 Jeffrey Lang
 5 years ago
 Views:
Transcription
1 9 Area, Perimeter and Volume D Shapes The following table gives the names of some 2D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right angles ( 90 ) Opposite sides have the same length Square All the sides have the same length All angles are right angles ( 90 ) Parallelogram Opposite sides have the same length Rhombus All the sides have the same length Diagonals bisect at right angles Trapezium Kite Diagonals intersect at right angles Isosceles Triangle Two sides have the same length and the angles opposite these two sides are equal Equilateral Triangle All angles are 60 1
2 9.1 MEP Y9 Practice Book B Example 1 Draw the lines of symmetry of an equilateral triangle. Solution There are 3 lines of symmetry, as shown in the diagram. They join each vertex (corner) to the midpoint of the opposite side. Example 2 Name each of the following shapes: Solution 1 This is a rhombus because all the sides have the same lengths. This is an isosceles triangle because two of the angles are the same size. Example 3 State the order of rotational symmetry of: a trapezium, a parallelogram. Solution 1 2 (unless the parallelogram happens to be a square, in which case the order of rotational symmetry would be 4). 2
3 Exercises 1. Name each of the following shapes: (c) (d) (e) (f) cm Draw diagrams to show the lines of symmetry of: a kite, a square, (c) a rectangle, (d) an isosceles triangle. 3. How many lines of symmetry are there for: a parallelogram, a rhombus? 4. State whether each of the following statements is true or false. A square is also a rhombus. A square is also a kite. (c) A rectangle is also a kite. (d) A parallelogram is also a kite. (e) A rectangle is also a parallelogram. 5. Write down the order of rotational symmetry of: a rhombus, a square, (c) an isosceles triangle, (d) an equilateral triangle, (e) a kite. 3
4 9.1 MEP Y9 Practice Book B 6. A triangle has one line of symmetry. What type of triangle is it? 7. Draw a trapezium that has: one line of symmetry, no lines of symmetry. 8. A rightangled triangle is also an isosceles triangle. What sizes are the other angles in this triangle? 9. For a semicircle: draw a diagram to show its lines of symmetry, state its order of rotational symmetry. 10. Draw a diagram to show the lines of symmetry of a regular pentagon. State the order of rotational symmetry of a regular octagon. 11. Rosemary drew these rectangles using a computer: D A B C Rectangle A has width 3 and length 5: 3 5 The computer repeated these instructions to draw the other rectangles: new width = previous width 2 new length = previous length + previous width Copy and complete this table. width length rectangle A 3 5 rectangle B rectangle C rectangle D (KS3/94/Ma/35/P1) 4
5 9.2 Area of Special Shapes In this section we calculate the area of various shapes. Area of a circle = π r 2 r Area of a triangle = 1 2 bh b h (h is perpendicular height) Area of a parallelogram = bh h b Example 1 Calculate the area of the triangle shown. Solution Area = = 12 cm 2 Example 2 Calculate the area of a circle with diameter 10 m. Solution Radius = 10 2 = 5 m Area = π 5 2 = m 2 = 78.5 m 2 (to 3 significant figures) Example 3 Calculate the area of the shape shown: 8 m 5 4 m
6 9.2 MEP Y9 Practice Book B Solution Area of rectangle = 4 8 = 32 m 2 Radius of semicircle = 4 2 = 2 m Area of semicircle = 1 2 π 2 2 = m 2 Total area = = m 2 = 38.3 m 2 (to 3 significant figures) Example 4 The diagram shows a piece of card in the shape of a parallelogram, that has had a circular hole cut in it. Calculate the area of the shaded part. 11 cm Solution Area of parallelogram = 11 6 = 66 c m 2 Radius of circle = 4 2 = 2 cm Area of circle = π 2 2 = c m 2 Area of shape = = cm 2 = 53.4 c m 2 (to 3 significant figures) 6
7 Exercises 1. Calculate the area of each of the following shapes: 5 m 3 cm 9 m (c) (d) 6.5 m 6.2 cm 6 m 2. Calculate, giving your answers correct to 3 significant figures, the area of a circle with: radius 6 m, diameter 20 cm, (c) diameter 9 cm. 3. Calculate the area of each of the following shapes, giving your answers correct to 3 significant figures: 2 cm 3 cm 2 cm 12 cm 4 m (c) 8 m (d) 1 10 m 7
8 9.2 MEP Y9 Practice Book B 4. Calculate, giving your answers correct to 3 significant figures, the area of the semicircle with: radius 30 cm, diameter 14 mm. 5. A circle of radius is cut into 6 parts of equal size, as shown in the diagram. Calculate the area of each part, giving your answer correct to 2 decimal places. 6. Giving your answers correct to 3 significant figures, calculate the area of each of the following shapes. Each of the curved parts is a semicircle. 9 cm 8 m 8 m 9 cm 8 m (c) (d) 9 mm 9 mm 11 cm 7. A rectangular metal plate is shown in the diagram. Four holes of diameter 8 mm are drilled in the plate. Calculate the area of the remaining metal, giving your answer correct to 2 decimal places. 40 mm 20 mm 8
9 8. Calculate the area of the shape shown, giving your answer correct to 1 decimal place. 2 cm 1 cm 1cm 2 cm 2 cm 2 cm 9. The area that has been shaded in the diagram has an area of Calculate the diameter of the semicircular hole, giving your answer to the nearest millimetre. 9 cm 10. The diagram shows the lid of a child's shapesorter box. Calculate the area of the lid, giving your answer correct to 1 decimal place cm cm 1.2 cm 3 cm 10. 9
10 9.2 MEP Y9 Practice Book B 11. Each shape in this question has an area of 10 cm 2. No diagram is drawn to scale. Calculate the height of the parallelogram. height Calculate the length of the base of the triangle. 2 cm base (c) What might be the values of h, a and b in this trapezium? What else might be the values of h, a and b? a h b 4 x + 2 (d) Look at this rectangle: area = 10 cm 2 Calculate the value of x and use it to find the length and width of the rectangle. Show your working. 12. This shape is designed using 3 semicircles. 10 x 1 (KS3/98/Ma/Tier 57/P1) The radii of the semicircles are 3 a, 2 a and a. 3a 2a a Find the area of each semicircle, in terms of a and π, and show that 2 the total area of the shape is 6π a. 2 The area, 6π a, of the shape is 12 cm 2. Write an equation in the form a =..., leaving your answer in terms of π. Show your working and simplify your equation. (KS3/98/Ma/Tier 68/P1) 10
11 13. Calculate the area of this triangle. 2 NOT TO SCALE 7 cm Show your working. (KS3/97/Ma/Tier 57/P2) 14. A box for coffee is in the shape of a hexagonal prism. One end of the box is shown below. Coffee 10 cm NOT TO SCALE Each of the 6 triangles in the hexagon has the same dimensions. Calculate the total area of the hexagon. Show your working. The box is 10 cm long. 10 cm Coffee After packing, the coffee fills 80% of the box. How many grams of coffee are in the box? (The mass of 1 cm 3 of coffee is 0.5 grams.) Show your working. (c) A 227 g packet of the same coffee costs How much per 100 g of coffee is this? Show your working (KS3/98/Ma/Tier 57/P2) 11
12 7 MEP Y9 Practice Book B 9.3 Perimeter of Special Shapes In this section we calculate the perimeters of various shapes. The perimeter of a circle is referred to as the 'circumference'. The circumference, C, of a circle = 2π r or π d where r is the radius and d is the diameter of the circle. Example 1 Calculate the circumference of a circle with radius. Solution Using the formula, C = 2π r, gives C = 2 π 8 = = 50.3 cm (to 3 significant figures) Example 2 The diagram shows a semicircle of diameter 12 cm. Calculate the perimeter of the semicircle. Solution 12 cm Length of curve = π 12 2 = cm Straight edge = 12 cm Total perimeter = Example 3 = cm = 30. (to 3 significant figures.) The diagram shows a shape that is made up of a rectangle, a triangle and a semicircle. Calculate its perimeter. 7 cm 7 cm Solution Length of curve = π 7 2 = cm 12
13 Total perimeter = = cm = 39.0 cm (to 3 significant figures) Exercises 1. Giving your answers correct to 3 significant figures, calculate the circumference of a circle with: radius 6 m, diameter 1, (c) radius 8 mm. 2. Calculate the perimeter of each of the following shapes: 9 cm 10 cm (c) (d) Giving your answer correct to 3 significant figures, calculate the perimeter of the semicircle shown. 1 13
14 9.3 MEP Y9 Practice Book B 4. A circle of radius is cut into four equal parts as shown in the diagram: Calculate the circumference of the original circle, giving your answer correct to 2 decimal places. Calculate the perimeter of each of the 4 parts, giving your answers correct to 2 decimal places. 5. Calculate the perimeter of each of the following shapes, giving your answers correct to 1 decimal place. The circular parts are either semicircles or quarters of circles. 1 cm 2 cm (c) 15 m (d) 7 cm 2 cm 10 m 10 cm 10 cm 15 m 10 cm 6. Calculate the perimeter of each of the following shapes: 9 cm 3 cm 14
15 7. A square has an area of 36 m 2. Calculate its perimeter. 8. Calculate the perimeter of this shape, giving your answer correct to the nearest centimetre: 1 m 1 m 1 m 6 m 1 m 10 m 1 m 1 m 1 m 1 m 9. A circle of radius 32 cm is cut into 8 equal parts, as shown in the diagram. Calculate the perimeter of each part, giving your answer correct to the nearest millimetre. 10. The total perimeter of a semicircle is 37 cm. Calculate the radius of the semicircle, giving your answer correct to the nearest millimetre. s s 11. The perimeter of this shape is 3t + 2s. t t p = 3t + 2s t Write an expression for the perimeters of each of these shapes. Write each expression in its simplest form. b c c a a b b a e (c) d d (d) e f f e f f e (KS3/95/Ma/35/P1) 15
16 9.3 MEP Y9 Practice Book B 12. Each side of this hexagon is 1 cm long. The shaded shape below is made from 7 hexagon tiles. Write down the perimeter of the shaded shape. On a copy of the following diagram, shade a shape made with 7 tiles which has a smaller perimeter. 16
17 (c) (d) (e) Explain what made its perimeter less than the perimeter of the first shape. On a copy of the following diagram, shade a shape made with 7 tiles which has the biggest possible perimeter. Explain what made your shape have the biggest possible perimeter. (KS3/94/Ma/35/P2) 17
18 9.3 MEP Y9 Practice Book B 13. Wyn and Jay are using their wheelchairs to measure distances. The large wheel on Wyn's wheelchair has a diameter of 60 cm. Wyn pushes the wheel round exactly once. Calculate how far Wyn has moved. Show your working. The large wheel on Jay's wheelchair has a diameter of 52 cm. Jay moves her wheelchair forward 950 cm. Calculate how many times the large wheel goes round. Show your working. (KS3/96/Ma/Tier 57/P2) 14. A circle has a radius of 1. Calculate the area of the circle. Show your working. 1 A different circle has a circumference of 120 cm. What is the radius of the circle? Show your working. (KS3/99/Ma/Tier 57/P2) 18
19 9.4 Surface Area and Volume of 3D Shapes In this section we calculate the volume and surface area of 3D shapes such as cubes, cuboids, prisms and cylinders. Cube x x x Volume = x 3 Surface area = 6 x 2 z Cuboid y Volume = xyz Surface area = 2xy+2xz+2yz x r Cylinder h Volume =πr 2 h Area of curved surface =2πrh Area of each end =πr 2 Total surface area = 2 π rh+ 2π r 2 Prism A l A prism has a uniform crosssection Volume = area of cross section length = Al 19
20 9.4 MEP Y9 Practice Book B Example 1 Calculate the volume of the cuboid shown. Calculate the surface area of the cuboid shown. 5 m Solution Volume = m = 360 m 3 4 m ( ) + ( ) + ( ) Surface area = Example 2 = = 364 m 2 Calculate the volume and total surface area of the cylinder shown. Solution 2 Volume = π r h 2 = π 4 6 = cm 3 = 96 π = 302 cm 3 (to 3 significant figures) Area of curved surface = 2π rh = 2 π 4 6 = 48π = Area of each end = π r 2 = π 4 2 = 16π = ( ) Total surface area = = cm 2 = 251 cm 2 (to 3 significant figures) Note: From the working we can see that the area of the curved surface is 48π, and that the area of each end is 16π. The total surface area is therefore 48π+ 2 16π 80π ( ) = =. cm 2 = 251 cm 2 (to 3 significant figures) 20
21 Example 3 Calculate the volume of this prism. Solution Area of end of prism = cm = 2 2 Volume of prism = = 240 cm 3 Exercises 1. Calculate the volume and surface area of each of the following cuboids: 7 m 2 cm 5 m 4 m 2. Giving your answers correct to 3 significant figures, calculate the volume and total surface area of each of the following cylinders: 10 cm 21
22 9.4 MEP Y9 Practice Book B 3. Calculate the volume of each of the following prisms: 4 m 7 cm cm 3 m 6 m 4. Calculate the volume and surface area of the following prism: 2 m 2.5 m 1.5 m 10 m 5. The diagram shows a wooden block that has had a hole drilled in it. The diameter of the hole is 2 cm. Calculate the volume of this solid, giving your answer correct to 2 decimal places. 6. A concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5 m, 3 m and 0.4 m. The pillars have diameter 0.4 m and height 2 m. Calculate the total volume of concrete needed to make the beam and the pillars. Round your answer to a sensible level of accuracy. 22
23 7. The diagram shows the crosssection of a pipe of length 50 cm. The inner diameter of the pipe is 20 cm and the outer diameter is 30 cm. Calculate the volume of metal needed to make the pipe. Round your answer to a sensible level of accuracy. Calculate the total surface area of the pipe, including the inside surface. Round your answer to a sensible level of accuracy. 8. The diagram shows a prism. The crosssection of the prism consists of a rectangle and a semicircle. Calculate the volume 3 cm of the prism. Give your answer to the nearest cm 3. Calculate the total surface area of the prism. Give your answer to the nearest cm cm 9. The volume of the prism shown is 720 mm 3. 9 mm 10 mm 6 mm 8 mm Determine the length of the prism. Calculate the surface area of the prism. 23
24 9.4 MEP Y9 Practice Book B 10. A cylinder has a diameter of 12 cm and a curved surface area of 132π or 41 2 (to 3 significant figures). Determine the height of the cylinder. Calculate the volume of the cylinder, giving your answer to the nearest cm These cuboids are made from small cubes. Write how many small cubes there are in each cuboid. The first is done for you. 2 (i) 2 (ii) (iii) 3 Cube (i) is made from 12 small cubes (iv) This shape is made with two cuboids. Write how many cubes there are in this shape (KS3/98/Ma/Tier 35/P1) 24
25 12. What is the volume of this standard size box of salt? 10 cm Salt Standard Size What is the volume of this special offer box of salt, which is 20% bigger? 20% more Salt Special Offer The standard size box contains enough salt to fill up 10 salt pots. Salt Salt Salt Salt Salt Salt Salt Salt Salt Salt (c) How many salt pots may be filled up from the special offer box of salt? (KS3/96/Ma/Tier 57/P2) 13. Look at this triangle. Show working to explain why angle x must be a right angle. NOT TO SCALE 10 cm x What is the volume of this prism? You must show each step in your working. 7 cm 10 cm NOT TO SCALE 25
26 9.4 MEP Y9 Practice Book B (c) Prisms A and B have the same crosssectional area. A 3 cm B NOT TO SCALE Copy and complete the table: Prism A Prism B height 3 cm volume 200 cm 3... cm 3 (KS3/99/Ma/Tier 57/P1) 14. TJ's Cat Food is sold in tins shaped like this. Each tin has an internal height of. The area of the lid of the tin is 3 2. Work out the volume of cat food that the tin contains. The label that goes round the tin overlaps by 1 cm. 1 cm NOT TO SCALE The area of the label is Work out the distance around the tin. Show your working. 26
27 TJ's Cat Food plans to use tins that are the shape of cylinders. The internal measurements of a tin are shown. (c) Work out the volume of cat food that the tin contains. Show your working. (KS3/95/Ma/Levels 57/P2) 27
16 Circles and Cylinders
16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two
More informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationGAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book
GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18
More informationCHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS
CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change
More informationMENSURATION. Definition
MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
More informationThe formulae for calculating the areas of quadrilaterals, circles and triangles should already be known : Area = 1 2 D x d CIRCLE.
Revision  Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known : SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationExercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of
More informationUnit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
More informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationArea of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
More informationSURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
More informationWhich two rectangles fit together, without overlapping, to make a square?
SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has
More informationVOLUME AND SURFACE AREAS OF SOLIDS
VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b
More informationAngle  a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle  a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationMensuration. The shapes covered are 2dimensional square circle sector 3dimensional cube cylinder sphere
Mensuration This a mixed selection of worksheets on a standard mathematical topic. A glance at each will be sufficient to determine its purpose and usefulness in any given situation. These notes are intended
More informationArea of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
More informationPizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More informationCIRCUMFERENCE AND AREA OF A CIRCLE
CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given
More informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 91.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
More informationBy the end of this set of exercises, you should be able to:
BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of
More informationApplications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
More information12 Surface Area and Volume
12 Surface Area and Volume 12.1 ThreeDimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids
More informationAlgebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More informationChapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
More informationGAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement
GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
More informationSolids. Objective A: Volume of a Solids
Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular
More informationPerimeter is the length of the boundary of a two dimensional figure.
Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationGCSE Revision Notes Mathematics. Volume and Cylinders
GCSE Revision Notes Mathematics Volume and Cylinders irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;
More informationGAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
More informationCHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.
TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has
More informationArea. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
More informationME 111: Engineering Drawing
ME 111: Engineering Drawing Lecture # 14 (10/10/2011) Development of Surfaces http://www.iitg.ernet.in/arindam.dey/me111.htm http://www.iitg.ernet.in/rkbc/me111.htm http://shilloi.iitg.ernet.in/~psr/ Indian
More information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS  SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More information2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
More information121 Representations of ThreeDimensional Figures
Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 121 Representations of ThreeDimensional Figures Use isometric dot paper to sketch each prism. 1. triangular
More informationUNIT H1 Angles and Symmetry Activities
UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationDŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet
Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils
More informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More informationSA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
More informationSGS4.3 Stage 4 Space & Geometry Part A Activity 24
SGS4.3 Stage 4 Space & Geometry Part A Activity 24 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners
More information1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?
Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is
More informationArea is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
More informationALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC
ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC
More informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfdprep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationWednesday 15 January 2014 Morning Time: 2 hours
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number
More informationGCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.
Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How
More informationHow To Find The Area Of A Shape
9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.
More informationSurface Area Quick Review: CH 5
I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationLesson 22. Circumference and Area of a Circle. Circumference. Chapter 2: Perimeter, Area & Volume. Radius and Diameter. Name of Lecturer: Mr. J.
Lesson 22 Chapter 2: Perimeter, Area & Volume Circumference and Area of a Circle Circumference The distance around the edge of a circle (or any curvy shape). It is a kind of perimeter. Radius and Diameter
More informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
More informationMATHEMATICS FOR ENGINEERING BASIC ALGEBRA
MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 4 AREAS AND VOLUMES This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.
More informationTeeJay Publishers General Homework for Book 3G Ch 9  circles. Circles
Circles Homework Chapter 9 Exercise 1 1. For each of these circles, say whether the dotted line is a radius or a diameter : (d) 2. Use two letters to name the line which is a diameter in this circle.
More informationStudent Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)
Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 111: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationSimilar shapes. 33.1 Similar triangles CHAPTER. Example 1
imilar shapes 33 HTR 33.1 imilar triangles Triangle and triangle have the same shape but not the same size. They are called similar triangles. The angles in triangle are the same as the angles in triangle,
More informationGEOMETRIC MENSURATION
GEOMETRI MENSURTION Question 1 (**) 8 cm 6 cm θ 6 cm O The figure above shows a circular sector O, subtending an angle of θ radians at its centre O. The radius of the sector is 6 cm and the length of the
More informationPlatonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:
Solid Geometry Solid Geometry is the geometry of threedimensional space, the kind of space we live in. Three Dimensions It is called threedimensional or 3D because there are three dimensions: width,
More informationGrade 8 Mathematics Geometry: Lesson 2
Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationCircumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
More informationWhat You ll Learn. Why It s Important
These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More informationHiker. A hiker sets off at 10am and walks at a steady speed for 2 hours due north, then turns and walks for a further 5 hours due west.
Hiker A hiker sets off at 10am and walks at a steady speed for hours due north, then turns and walks for a further 5 hours due west. If he continues at the same speed, what s the earliest time he could
More informationPaper 1. Mathematics test. Calculator not allowed. First name. Last name. School KEY STAGE TIER
Ma KEY STAGE 3 TIER 4 6 2005 Mathematics test Paper 1 Calculator not allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your
More informationSandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.
Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.
More informationPaper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7
Ma KEY STAGE 3 Mathematics test TIER 5 7 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
More informationAssessment For The California Mathematics Standards Grade 4
Introduction: Summary of Goals GRADE FOUR By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationIWCF United Kingdom Branch
IWCF United Kingdom Branch Drilling Calculations Distance Learning Programme Part 2 Areas and Volumes IWCF UK Branch Distance Learning Programme  DRILLING CALCULATIONS Contents Introduction Training objectives
More information7 th Grade Study guide IV Partial Remember to practice the constructions that are not part of this guide.
7 th Grade Study guide IV Partial Remember to practice the constructions that are not part of this guide. 1. Which figure shows one point? a. S R c. D C b. Q d. F G 2. Which name describes the line? G
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationGeometry Notes VOLUME AND SURFACE AREA
Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate
More informationPaper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 4 6
Ma KEY STAGE 3 Mathematics test TIER 4 6 Paper 1 Calculator not allowed First name Last name School 2007 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationPerimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationFinding Volume of Rectangular Prisms
MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of threedimensional composite shapes.
More information2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?
MATH 206  Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of
More informationShow that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.
Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional
More information3D shapes. Level A. 1. Which of the following is a 3D shape? A) Cylinder B) Octagon C) Kite. 2. What is another name for 3D shapes?
Level A 1. Which of the following is a 3D shape? A) Cylinder B) Octagon C) Kite 2. What is another name for 3D shapes? A) Polygon B) Polyhedron C) Point 3. A 3D shape has four sides and a triangular
More information2014 2015 Geometry B Exam Review
Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists
More informationArea and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
More informationCalculating the Surface Area of a Cylinder
Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping
More informationCalculate the circumference of a circle with radius 5 cm. Calculate the area of a circle with diameter 20 cm.
RERTIES F CIRCLE Revision. The terms Diameter, Radius, Circumference, rea of a circle should be revised along with the revision of circumference and area. Some straightforward examples should be gone over
More information2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
More informationPerimeter, Area and Volume of Regular Shapes
Perimeter, Area and Volume of Regular Sapes Perimeter of Regular Polygons Perimeter means te total lengt of all sides, or distance around te edge of a polygon. For a polygon wit straigt sides tis is te
More information