# 9 Area, Perimeter and Volume

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 9 Area, Perimeter and Volume D Shapes The following table gives the names of some 2-D 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 right-angled 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/3-5/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 semi-circular hole, giving your answer to the nearest millimetre. 9 cm 10. The diagram shows the lid of a child's shape-sorter 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 semi-circles. 10 x 1 (KS3/98/Ma/Tier 5-7/P1) The radii of the semi-circles are 3 a, 2 a and a. 3a 2a a Find the area of each semi-circle, 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 6-8/P1) 10

11 13. Calculate the area of this triangle. 2 NOT TO SCALE 7 cm Show your working. (KS3/97/Ma/Tier 5-7/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 5-7/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/3-5/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/3-5/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 5-7/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 5-7/P2) 18

19 9.4 Surface Area and Volume of 3-D Shapes In this section we calculate the volume and surface area of 3-D 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 cross-section 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 cross-section 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 cross-section 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 3-5/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 5-7/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 cross-sectional 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 5-7/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 5-7/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

### Working in 2 & 3 dimensions Revision Guide

Tips for Revising Working in 2 & 3 dimensions Make sure you know what you will be tested on. The main topics are listed below. The examples show you what to do. List the topics and plan a revision timetable.

### Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

### Begin recognition in EYFS Age related expectation at Y1 (secure use of language)

For more information - http://www.mathsisfun.com/geometry Begin recognition in EYFS Age related expectation at Y1 (secure use of language) shape, flat, curved, straight, round, hollow, solid, vertexvertices

### LESSON SUMMARY. Measuring Shapes

LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given

### Shape 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

### GAP 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

### CHAPTER 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

### MENSURATION. 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

### CHAPTER 27 AREAS OF COMMON SHAPES

EXERCISE 113 Page 65 CHAPTER 7 AREAS OF COMMON SHAPES 1. Find the angles p and q in the diagram below: p = 180 75 = 105 (interior opposite angles of a parallelogram are equal) q = 180 105 0 = 35. Find

### A factor is a whole number that. Name 6 different quadrilaterals. The radius of a circle. What is an axis or a line of symmetry in a 2-D shape?

BOND HOW TO DO 11+ MATHS MATHS FACTS CARDS 1 2 3 4 A factor is a whole number that Name 6 different quadrilaterals. The radius of a circle is What is an axis or a line of symmetry in a 2-D shape? 5 6 7

### PERIMETERS AND AREAS

PERIMETERS AND AREAS 1. PERIMETER OF POLYGONS The Perimeter of a polygon is the distance around the outside of the polygon. It is the sum of the lengths of all the sides. Examples: The perimeter of this

### Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

### Target To know the properties of a rectangle

Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

### 10.1: Areas of Parallelograms and Triangles

10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a

### The 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

### LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

### Q1. The grid below is made of right-angled triangles like this: Shade triangles on the grid to make a quadrilateral.

Q1. The grid below is made of right-angled triangles like this: Shade triangles on the grid to make a quadrilateral. Your quadrilateral must have an area of 24 cm 2 and a perimeter of 26 cm. Page 1 of

### PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

### The Area is the width times the height: Area = w h

Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

### Perimeter and area formulas for common geometric figures:

Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,

### Circle Theorems. Angles at the circumference are equal. The angle in a semi-circle is x The angle at the centre. Cyclic Quadrilateral

The angle in a semi-circle is 90 0 Angles at the circumference are equal. A B They must come from the same arc. Look out for a diameter. 2x Cyclic Quadrilateral Opposite angles add up to 180 0 A They must

### Geometry 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

### 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?

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

### Area 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

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### Unit 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

### 2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters

GEOMETRY Vocabulary 1. Adjacent: Next to each other. Side by side. 2. Angle: A figure formed by two straight line sides that have a common end point. A. Acute angle: Angle that is less than 90 degree.

### Angles 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,

### 15. PRISMS AND CYLINDERS

15. PRISMS AND CYLINDERS 15-1 Drawing prisms 2 15-2 Modelling prisms 4 15-3 Cross-sections of prisms 6 15-4 Nets of prisms 7 15-5 Euler's formula 8 15-6 Stacking prisms 9 15-7 Cylinders 10 15-8 Why is

### VOLUME 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

### Area 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

### Name Revision Sheet 1

Name Revision Sheet 1 1 What is 8? Show your working 11 Solve the equation y 1 Round 79 to the nearest 10. 1 Expand ( x 1 0 ) Use BIDMAS to work out 5 1 How many lines of symmetry does a square have? 1

### 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron

### Drawing shapes in Word. Information sheet. A How to draw basic shapes. To draw a rectangle

Drawing shapes in Word You can use Word to draw tiling patterns, scale diagrams and all sorts of other illustrations. This activity and others will show you how to do this. Information sheet A How to draw

### Geometry 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

### Which 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

### Pizza! 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

### Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

### SURFACE 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

### SOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier

Mathematics Revision Guides Solid Shapes Page 1 of 19 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SOLID SHAPES Version: 2.1 Date: 10-11-2015 Mathematics Revision Guides Solid

### CIRCUMFERENCE 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

### Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

### 23. [Perimeter / Area]

3. [Perimeter / rea] Skill 3. Calculating the perimeter of polygons (). MM5. 33 44 MM6. 33 44 Convert all measurements to the same unit. Find and label the length of all sides. dd together all side lengths.

### 3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks)

EXERCISES: Triangles 1 1. The perimeter of an equilateral triangle is units. How many units are in the length 27 of one side? (Mathcounts Competitions) 2. In the figure shown, AC = 4, CE = 5, DE = 3, and

### 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

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

### Dyffryn School Ysgol Y Dyffryn Mathematics Faculty

Dyffryn School Ysgol Y Dyffryn Mathematics Faculty Formulae and Facts Booklet Higher Tier Number Facts Sum This means add. Difference This means take away. Product This means multiply. Share This means

### Area 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

### Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

### DIFFERENTIATION OPTIMIZATION PROBLEMS

DIFFERENTIATION OPTIMIZATION PROBLEMS Question 1 (***) 4cm 64cm figure 1 figure An open bo is to be made out of a rectangular piece of card measuring 64 cm by 4 cm. Figure 1 shows how a square of side

### SHAPE, SPACE AND MEASURES

SHAPE, SPACE AND MEASURES Pupils should be taught to: Use accurately the vocabulary, notation and labelling conventions for lines, angles and shapes; distinguish between conventions, facts, definitions

### Circumference and area of a circle

c Circumference and area of a circle 22 CHAPTER 22.1 Circumference of a circle The circumference is the special name of the perimeter of a circle, that is, the distance all around it. Measure the circumference

### GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book

GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas

### Mensuration. The shapes covered are 2-dimensional square circle sector 3-dimensional 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

### NCERT. Area of the circular path formed by two concentric circles of radii. Area of the sector of a circle of radius r with central angle θ =

AREA RELATED TO CIRCLES (A) Main Concepts and Results CHAPTER 11 Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height

Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side

### 2006 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

### GAP 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 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4

### Perimeter 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

### PRACTICAL GEOMETRY SYMMETRY AND VISUALISING SOLID SHAPES NCERT

UNIT 12 PRACTICAL GEOMETRY SYMMETRY AND VISUALISING SOLID SHAPES (A) Main Concepts and Results Let a line l and a point P not lying on it be given. By using properties of a transversal and parallel lines,

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

### (a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

### Chapter 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

### By 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

### Solids. 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

### Applications 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

### 43 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

### GCSE 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;

### Algebra 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:

### YOU 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

### Length, perimeter and area 3.1. Example

3.1 Length, perimeter and area Kno and use the names and abbreviations for units of length and area Be able to measure and make a sensible estimate of length and area Find out and use the formula for the

### Dŵr 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

### 28. [Area / Volume] cm 2. in = =

8. [ / Volume] Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). Count the number of fully shaded squares on the grid. If necessary add on the number of half

### Q1. Here is a flag. Calculate the area of the shaded cross. Q2. The diagram shows a right-angled triangle inside a circle.

Q1. Here is a flag. Calculate the area of the shaded cross. 2 marks Q2. The diagram shows a right-angled triangle inside a circle. The circle has a radius of 5 centimetres. Calculate the area of the triangle.

### Area. 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.

### Lesson 21. Chapter 2: Perimeter, Area & Volume. Lengths and Areas of Rectangles, Triangles and Composite Shapes

ourse: HV Lesson hapter : Perimeter, rea & Volume Lengths and reas of Rectangles, Triangles and omposite Shapes The perimeter of a shape is the total length of its boundary. You can find the perimeter

### Junior Math Circles November 18, D Geometry II

1 University of Waterloo Faculty of Mathematics Junior Math Circles November 18, 009 D Geometry II Centre for Education in Mathematics and Computing Two-dimensional shapes have a perimeter and an area.

### 39 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

### 10.1 Areas of Quadrilaterals and triangles

10.1 Areas of Quadrilaterals and triangles BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:. A rectangle with one side of

### 12 Surface Area and Volume

12 Surface Area and Volume 12.1 Three-Dimensional 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

### 15 Trigonometry Pythagoras' Theorem. Example 1. Solution. Example 2

15 Trigonometry 15.1 Pythagoras' Theorem MEP Y9 Practice Book B Pythagoras' Theorem describes the important relationship between the lengths of the sides of a right-angled triangle. Pythagoras' Theorem

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### CHAPTER 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

### National 4: Expressions and Formulae

Biggar High School Mathematics Department National 4 Pupil Booklet National 4: Expressions and Formulae Learning Intention Success Criteria I can simplify algebraic expressions. I can simplify and carry

### Unit 04: Fundamentals of Solid Geometry - Shapes and Volumes

Unit 04: Fundamentals of Solid Geometry - Shapes and Volumes Introduction. Skills you will learn: a. Classify simple 3-dimensional geometrical figures. b. Calculate surface areas of simple 3-dimensional

### Geometry 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

### PERIMETER AND AREA OF PLANE FIGURES

PERIMETER AND AREA OF PLANE FIGURES Q.. Find the area of a triangle whose sides are 8 cm, 4 cm and 30 cm. Also, find the length of altitude corresponding to the largest side of the triangle. Ans. Let ABC

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### SA 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.

### SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4

SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners

### UK Junior Mathematical Olympiad 2016

UK Junior Mathematical Olympiad 206 Organised by The United Kingdom Mathematics Trust Tuesday 4th June 206 RULES AND GUIDELINES : READ THESE INSTRUCTIONS CAREFULLY BEFORE STARTING. Time allowed: 2 hours.

### Su.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)

MA.912.G.2 Geometry: Standard 2: Polygons - Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures

Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

### BASIC GEOMETRY GLOSSARY

BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that

### Chapter 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

### 12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h

Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the

### Perimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this.

UNIT 10 Perimeter and Area An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. 3 UNIT 10 PERIMETER AND AREA You can find geometric shapes in