CHAPTER 27 AREAS OF COMMON SHAPES

Size: px
Start display at page:

Download "CHAPTER 27 AREAS OF COMMON SHAPES"

Transcription

1 EXERCISE 113 Page 65 CHAPTER 7 AREAS OF COMMON SHAPES 1. Find the angles p and q in the diagram below: p = = 105 (interior opposite angles of a parallelogram are equal) q = = 35. Find the angles r and s in the diagram below: r = = 1 (the 38 angle is the alternate angle between parallel lines) s = = Find the angle t in the diagram below: t = = , John Bird

2 EXERCISE 11 Page Name the types of quadrilateral shown in (i) to (iv) below, and determine for each (a) the area, and (b) the perimeter. (i) Rhombus (a) Area = 3.5 = 1 cm (b) Perimeter = = 16 cm (ii) Parallelogram (a) Area = 30 6 = 180 mm (b) Perimeter = ( ) = 80 mm (iii) Rectangle (a) Area = = 3600 mm (b) Perimeter = ( 10) + ( 30) = 300 mm (iv) Trapezium = 190 cm (a) Area = ( ) (b) Perimeter = ( ) + ( + 10 ) = = 6.91 cm 39 01, John Bird

3 . A rectangular plate is 85 mm long and mm wide. Find its area in square centimetres. Area of plate = length width = 85 mm = 8.5. cm = 35.7 cm 3. A rectangular field has an area of 1. hectares and a length of 150 m. If 1 hectare = m, find (a) its width, and (b) the length of a diagonal. Area of field = 1. ha = m = m (a) Area = length width from which, width = (b) By Pythagoras, length of diagonal = ( ) area 1000 = = 80 m length = 170 m. Find the area of a triangle whose base is 8.5 cm and perpendicular height 6. cm. Area of triangle = 1 base perpendicular height = = 7. cm 5. A square has an area of 16 cm. Determine the length of a diagonal. Let each side of square = x, then area = x = 16 from which, x = 16 Using Pythagoras theorem, x + x = d where d is the length of the diagonal i.e. ( 16 ) + ( 16 ) = d i.e = d from which, diagonal, d = 3 = 18 cm 6. A rectangular picture has an area of 0.96 m. If one of the sides has a length of 800 mm, calculate, in millimetres, the length of the other side. 0 01, John Bird

4 Area of picture = length width from which, width = area length mm = = 100 mm 800 mm 7. Determine the area of each of the angle iron sections shown below. (a) Area = (7 ) + (1 1) = = 9 cm (b) Area = (30 8) + 10(5 8 6) + (6 50) = = 650 mm 8. The diagram shows a m wide path around the outside of a 1 m by 37 m garden. Calculate the area of the path. Area of path = (1 37) [(1 8) (37 8)] = = 560 m 9. The area of a trapezium is 13.5 cm and the perpendicular distance between its parallel sides is 3 cm. If the length of one of the parallel sides is 5.6 cm, find the length of the other parallel side. Area of a trapezium = 1 (sum of parallel sides) (perpendicular distance between the parallel sides) Hence, area of trapezium = 13.5 = 1 (5.6 + b) 3 where b is the unknown parallel side i.e. 7 = b 1 01, John Bird

5 i.e = 3b i.e. 10. = 3b and the unknown parallel side, b = 10. = 3. cm Calculate the area of the steel plate shown. Area of steel plate = (5 60) + (10 60)(5) + ( ) 5 + (50 5) + = = 6750 mm Determine the area of an equilateral triangle of side 10.0 cm. An equilateral triangle is shown below. Area of triangle = 1 base height By Pythagoras, h = 10.0 and h = = 8.66 cm 01, John Bird

6 Area of triangle = = 3.30 cm 1. If paving slabs are produced in 50 mm by 50 mm squares, determine the number of slabs required to cover an area of m. Number of slabs = 10 mm = The diagram shows a plan view of an office block to be built. The walls will have a height of 8 m, and it is necessary to make an estimate of the number of bricks required to build the walls. Assuming that any doors and windows are ignored in the calculation and that 8 bricks are required to build 1 m of wall, calculate the number of external bricks required. Length of outside wall = = 600 m Area of wall = = 800 m Number of external bricks required = = , John Bird

7 EXERCISE 115 Page A rectangular garden measures 0 m by 15 m. A 1 m flower border is made round the two shorter sides and one long side. A circular swimming pool of diameter 8 m is constructed in the middle of the garden. Find, correct to the nearest square metre, the area remaining. A sketch of a plan of the garden is shown below. Shaded area = (0 15) [(15 1) + (38 1) + (15 1) + π ( ) ] = 600 [ π] = = m = 8 m, correct to the nearest square metre. Determine the area of circles having (a) a radius of cm, (b) a diameter of 30 mm and (c) a circumference of 00 mm. (a) Area of circle = πr = π () = 16π = 50.7 cm π d (b) Area of circle = π (30) = = 900 π = mm c (c) Circumference, c = πr hence radius, r = π = 00 π = 100 π mm Area of circle = πr 100 = π π = 100 π = 3183 mm or cm 3. An annulus has an outside diameter of 60 mm and an inside diameter of 0 mm. Determine its area. 01, John Bird

8 Area of shaded part = area of large circle area of small circle = π D π d = π (D d ) = π (60 0 ) = 513 mm. If the area of a circle is 30 mm, find (a) its diameter and (b) its circumference. π d (a) Area of circle = π d hence 30 = 30 i.e. d 30 = and diameter, d = π π = = 0.19 mm (b) Circumference, c = πr = πd = π = 63.1 mm 5. Calculate the areas of the following sectors of circles: (a) radius 9 cm, angle subtended at centre 75 (b) diameter 35 mm, angle subtended at centre 8 37' (a) Area of sector = θ (πr ) = (π9 ) = 75 π = cm (b) If diameter = 35 mm, then radius, r = 35/ =17.5 mm, and 8 37 ' area of sector = ( π 17.5 ) ( 17.5 ) 360 π = ( π 17.5 ) = 19.9 mm 360 = 5 01, John Bird

9 6. Determine the shaded area of the template shown. Area of template = shaded area = (10 90) 1 ( 80) π = = 5773 mm 7. An archway consists of a rectangular opening topped by a semi-circular arch as shown below. Determine the area of the opening if the width is 1 m and the greatest height is m. The semicircle has a diameter of 1 m, i.e. a radius of 0.5 m. Hence, the archway shown is made up of a rectangle of sides 1 m by 1.5 m and a semicircle of radius 0.5 m. Thus, area of opening = (1.5 1) + ( ) 1 π 0.5 = = 1.89 m 8. The major axis of an ellipse is 00 mm and the minor axis 100 mm. Determine the area and perimeter of the ellipse. If the major axis = 00 mm, then the semi-major axis, a = 100 mm If the minor axis = 100 mm, then the semi-minor axis, b = 50 mm Hence, area of ellipse = πab = π(100)(50) = cm and perimeter of ellipse π(a + b) = π( ) = 150π = 71 cm 6 01, John Bird

10 9. If fencing costs 15 per metre, find the cost (to the nearest pound) of enclosing an elliptical plot of land which has major and minor diameter lengths of 10 m and 80 m Perimeter of ellipse = π(a + b) = π + = 100π m Hence, cost of fencing = π = 71 to the nearest pound 10. A cycling track is in the form of an ellipse, the axes being 50 m and 150 m, respectively, for the inner boundary, and 70 m and 170 m for the outer boundary. Calculate the area of the track Area of an ellipse = πab, hence area of cycle track = π π = π(135)(85) π(15)(75) = 6597 m 7 01, John Bird

11 EXERCISE 116 Page Calculate the area of a regular octagon if each side is 0 mm and the width across the flats is 8.3 mm. The octagon is shown sketched below and comprises eight triangles of base length 0 mm and perpendicular height 8.3/ Area of octagon = = 193 mm. Determine the area of a regular hexagon which has sides 5 mm. The hexagon is shown sketched below and comprises six triangles of base length 5 mm and perpendicular height h as shown. Tan 30 = 1.5 h from which, h = 1.5 tan 30 = 1.65 mm Hence, area of hexagon = = 16 mm 8 01, John Bird

12 3. A plot of land is in the shape shown below. Determine (a) its area in hectares (1 ha = 10 m ), and (b) the length of fencing required, to the nearest metre, to completely enclose the plot of land (a) Area of land = (30 10) + 1 ( 30) π + ( )( ) 1 + ( ) ( )( 15) = π [ ] = 9176 m = ha = ha 1 30 (b) Perimeter = ( π ) ( 70 0) = π = 56 m, to the nearest metre ( ) ( 0 15) , John Bird

13 EXERCISE 117 Page 7 1. The area of a park on a map is 500 mm. If the scale of the map is 1 to 0 000, determine the true area of the park in hectares (1 hectare = 10 m ) Area of park = ( ) ( ) m = ha = 80 ha 10. A model of a boiler is made, having an overall height of 75 mm corresponding to an overall height of the actual boiler of 6 m. If the area of metal required for the model is mm, determine, in square metres, the area of metal required for the actual boiler. The scale is :1 i.e. 80:1 Area of metal required for actual boiler = m ( 80 ) = 80 m 3. The scale of an Ordnance Survey map is 1:500. A circular sports field has a diameter of 8 cm on the map. Calculate its area in hectares, giving your answer correct to 3 significant figures. (1 hectare = 10m ) Area of sports field on map = ( 8) π d π = 10 m True area of sports field = ( 8) π π ( 8) 10 ( 500) 10 ( 500) m = ha 10 = 3.1 ha 50 01, John Bird

9 Area, Perimeter and Volume

9 Area, Perimeter and Volume 9 Area, Perimeter and Volume 9.1 2-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

More information

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?

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

More information

CIRCUMFERENCE AND AREA OF A CIRCLE

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

More information

VOLUME AND SURFACE AREAS OF SOLIDS

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

More information

43 Perimeter and Area

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

More information

Geometry Progress Ladder

Geometry Progress Ladder 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

More information

Geometry of 2D Shapes

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

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

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

More information

Perimeter is the length of the boundary of a two dimensional figure.

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

More information

By the end of this set of exercises, you should be able to:

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

More information

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

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

More information

Target To know the properties of a rectangle

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

More information

GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

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

More information

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 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

More information

Algebra Geometry Glossary. 90 angle

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:

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

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,

More information

UNIT H1 Angles and Symmetry Activities

UNIT 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 information

Postulate 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.

Postulate 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) 11-1: 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 information

2006 Geometry Form A Page 1

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

More information

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

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

More information

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 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 information

TeeJay Publishers General Homework for Book 3G Ch 9 - circles. Circles

TeeJay 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 information

Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

More information

Area. Area Overview. Define: Area:

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.

More information

16 Circles and Cylinders

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 information

MENSURATION. Definition

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

More information

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

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

More information

Applications for Triangles

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

More information

Wednesday 15 January 2014 Morning Time: 2 hours

Wednesday 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 information

Chapter 16. Mensuration of Cylinder

Chapter 16. Mensuration of Cylinder 335 Chapter 16 16.1 Cylinder: A solid surface generated by a line moving parallel to a fixed line, while its end describes a closed figure in a plane is called a cylinder. A cylinder is the limiting case

More information

Shape Dictionary YR to Y6

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

More information

Tallahassee Community College PERIMETER

Tallahassee Community College PERIMETER Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

More information

Geometry Unit 6 Areas and Perimeters

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

More information

Perimeter. 14ft. 5ft. 11ft.

Perimeter. 14ft. 5ft. 11ft. Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine

More information

Geometry and Measurement

Geometry 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 information

GEOMETRIC MENSURATION

GEOMETRIC 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 information

ME 111: Engineering Drawing

ME 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 information

Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area 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 information

CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session. Geometry, 17 March 2012 CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

More information

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student 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 information

Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse

Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse Pythagoras Theorem Page I can... 1... identify and label right-angled triangles 2... eplain Pythagoras Theorem 4... calculate the hypotenuse 5... calculate a shorter side 6... determine whether a triangle

More information

How To Find The Area Of A Shape

How 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 information

Area of Parallelograms (pages 546 549)

Area 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 information

CAMI Education linked to CAPS: Mathematics

CAMI 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 information

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 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 information

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.

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

More information

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

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

More information

Characteristics of the Four Main Geometrical Figures

Characteristics 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 information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE 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 information

39 Symmetry of Plane Figures

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

More information

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile. MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

More information

Calculating Area, Perimeter and Volume

Calculating 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 information

B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3

B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3 45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space

More information

Perimeter, Area, and Volume

Perimeter, 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 information

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

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

More information

Grade 8 Mathematics Geometry: Lesson 2

Grade 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 information

Surface Area Quick Review: CH 5

Surface 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 information

Hiker. 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 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 information

Calculating Perimeter

Calculating Perimeter Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle

More information

GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement

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

More information

Dŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet

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

More information

Calculate the circumference of a circle with radius 5 cm. Calculate the area of a circle with diameter 20 cm.

Calculate 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 information

Lesson 22. Circumference and Area of a Circle. Circumference. Chapter 2: Perimeter, Area & Volume. Radius and Diameter. Name of Lecturer: Mr. J.

Lesson 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 information

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS 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 information

Mensuration. The shapes covered are 2-dimensional square circle sector 3-dimensional cube cylinder sphere

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

More information

Lesson 9.1 The Theorem of Pythagoras

Lesson 9.1 The Theorem of Pythagoras Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius

More information

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

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

More information

Pizza! Pizza! Assessment

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

More information

Chapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem!

Chapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Chapter 11 Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret

More information

Assessment For The California Mathematics Standards Grade 4

Assessment 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 information

Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.

Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms. -NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has

More information

Unit 8 Angles, 2D and 3D shapes, perimeter and area

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

More information

Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures 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 information

Unit 7 Circles. Vocabulary and Formulas for Circles:

Unit 7 Circles. Vocabulary and Formulas for Circles: ccelerated G Unit 7 ircles Name & ate Vocabulary and Formulas for ircles: irections: onsider 1) Find the circumference of the circle. to answer the following questions. Exact: pproximate: 2) Find the area

More information

SURFACE AREA AND VOLUME

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

More information

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.

Circumference 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 information

Build your skills: Perimeter and area Part 1. Working out the perimeter and area of different shapes

Build your skills: Perimeter and area Part 1. Working out the perimeter and area of different shapes Working out the perimeter and area of different shapes This task has two parts. Part 1 In this part, you can brush up your skills and find out about perimeter and area. Part 2 In the second part, you can

More information

WEDNESDAY, 2 MAY 1.30 PM 2.25 PM. 3 Full credit will be given only where the solution contains appropriate working.

WEDNESDAY, 2 MAY 1.30 PM 2.25 PM. 3 Full credit will be given only where the solution contains appropriate working. C 500/1/01 NATIONAL QUALIFICATIONS 01 WEDNESDAY, MAY 1.0 PM.5 PM MATHEMATICS STANDARD GRADE Credit Level Paper 1 (Non-calculator) 1 You may NOT use a calculator. Answer as many questions as you can. Full

More information

13 PERIMETER AND AREA OF 2D SHAPES

13 PERIMETER AND AREA OF 2D SHAPES 13 PERIMETER AND AREA OF D SHAPES 13.1 You can find te perimeter of sapes Key Points Te perimeter of a two-dimensional (D) sape is te total distance around te edge of te sape. l To work out te perimeter

More information

11.3 Curves, Polygons and Symmetry

11.3 Curves, Polygons and Symmetry 11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon

More information

Geometry Final Exam Review Worksheet

Geometry Final Exam Review Worksheet Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.

More information

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 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 information

MCB4UW Optimization Problems Handout 4.6

MCB4UW Optimization Problems Handout 4.6 MCB4UW Optimization Problems Handout 4.6 1. A rectangular field along a straight river is to be divided into smaller fields by one fence parallel to the river and 4 fences perpendicular to the river. Find

More information

12-1 Representations of Three-Dimensional Figures

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

More information

Developing Conceptual Understanding of Number. Set J: Perimeter and Area

Developing Conceptual Understanding of Number. Set J: Perimeter and Area Developing Conceptual Understanding of Number Set J: Perimeter and Area Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Perimeter and Area Vocabulary perimeter area centimetres right angle Notes

More information

Geometry - Calculating Area and Perimeter

Geometry - Calculating Area and Perimeter Geometry - Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry

More information

Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

More information

IWCF United Kingdom Branch

IWCF 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 information

How to fold simple shapes from A4 paper

How to fold simple shapes from A4 paper How to fold simple shapes from 4 paper ndrew Jobbings www.arbelos.co.uk 18 February 2012 ontents Introduction 1 Square 2 Equilateral triangle 3 Rhombus 5 Regular hexagon 6 Kite 7 Why do the methods work?

More information

Inv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.

Inv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units. Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE

More information

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

More information

Estimating Angle Measures

Estimating Angle Measures 1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

More information

Mathematics (Project Maths Phase 1)

Mathematics (Project Maths Phase 1) 2012. M128 S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination, 2012 Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Time: 2 hours, 30

More information

Which two rectangles fit together, without overlapping, to make a square?

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

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE.

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

More information

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

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.

More information

Definitions, Postulates and Theorems

Definitions, Postulates and Theorems Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

" Angles ABCand DEFare congruent

 Angles ABCand DEFare congruent Collinear points a) determine a plane d) are vertices of a triangle b) are points of a circle c) are coplanar 2. Different angles that share a common vertex point cannot a) share a common angle side! b)

More information

Math 2201 Chapter 8 Review

Math 2201 Chapter 8 Review Olga Math 2201 Chapter 8 Review Multiple Choice 1. A 2 L carton of milk costs $3.26. What is the unit rate? a. $0.83/500 ml b. $3.27/2 L c. $0.61/L d. $1.63/L 2.. drove 346 km and used up 28.7 L of gas.

More information