FORM 1 Chapter 5 Perimeter, Area and Volume 2014

Form 1 [CHAPTER 5: PERIMETER, AREA & VOLUME]

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Chapter 5: Perimeter, Area and Volume 5.1 Calculating perimeter of simple shapes and compound shapes. What is perimeter? Perimeter is the distance around the outside edge of a flat object. Example1: Finding the perimeter of a rectangle: Method 1 Method 2 ________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

Answer: The perimeter of this rectangle is: _________ cm. Example 2: Finding the perimeter of a square: Method 1 Method 2 ________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

Answer: The perimeter of this square is: _________ cm.

6 cm

10 cm

7 cm



Example 3: Find the perimeter of the following triangle.

________________________________________________________________________

________________________________________________________________________

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Answer: The Perimeter of the triangle is: __________mm. Example 4: Find the perimeter of this shape if each square is 1 m by 1 m. ________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

Answer: The Perimeter is __________ m.



Example 5: Find the perimeter of the following compound shape. _______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

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Example 6: Find the perimeter of the following shape. ________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

Answer: The perimeter is _________m. Example 7: Find the perimeter of the following shape.

________________________________________________________________________

________________________________________________________________________

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5.2 Converting Units of Perimeter Converting between cm and mm. Converting mm to cm. 10 mm = 1 cm (We divided 10 by 10)

65 mm = 6.5 cm ( We divided 65 by 10)

85 mm = _________cm. 79mm = _________ cm. 8mm = _________cm.

Converting cm to mm. 1 cm = 10 mm

5 cm = 50 mm (We multiplied 5 by 10)

0.9 cm = 9mm (We multiplied 0.9 by 10)

0.08 cm = _________ mm. 69 cm = _________ mm. 0.45 cm = __________ mm.

mm cm

x 10

10



Converting between cm and m. Example 1: Converting from cm to m 98 cm = 0.98 m ( 98 100)

1005 cm = 10.05 m (1005 100)

cm m

56 cm

3 cm

Example 2: Converting from m to cm. 2 m = 200 cm ( 2 100)

0.5m = 50 cm ( 0.5 100)

m cm

0.0078 m

0.05 m

Converting between m and km.

cm m

100

100

m km

1000

1000



Example 1: Converting from m to km. 1456m = 1.456 km ( 1456 1000)

50 m = 0.05 km (50 1000)

m km

56m

13678m

Example 2: Converting from km to m. 2km = 2000 m

5.89 km = 5890 m

km m

0.04 km

0.009 km

Mixed Examples: 1. Fill in the following table:

mm cm m km

9000 mm

79 m

7 cm

2. Fill in the following table:

Pupil Height (m and cm)

Height (m)

Height (mm)

Isaac 1 m 56 cm Matthias 1.37 m Nathan 1345 mm



5.3 What is area? Finding area of a square/ rectangle and compound shapes. Area is the surface the 2D (flat) shape covers. It is measured in squared units. Some of these units are:

Squared millimeters (mm2) Squared centimeters (cm2) Squared meters (m2)

Squared kilometers (km2)



Finding the area of a SQUARE: The area of this square is 25 cm2 since it is made up of 25 squares having sides that are one centimeter long.

You can multiply the length (5cm) by the breadth (5cm).

Finding the area of a RECTANGLE. The area of this rectangle is 12 cm2 since it is made up of 12 squares having sides that are one centimeter long. You can multiply the length (2cm) by the breadth (6cm).

5 cm

5 cm

Area of Square = Length breadth = l b = 5 5

= 25 cm2

6 cm

2 cm



Finding the area of compound shapes.

Area of Rectangle = Length breadth = l b = 2 6

= 12 cm2

It costs 10 to pave one square metre of the patio



5.4 Area of a parallelogram. What is a parallelogram? A parallelogram is a quadrilateral (4 sided shape) Opposite sides are equal Opposite sides are parallel

Finding the area of a parallelogram: Let us first transform the parallelogram into a shape which we know how to find the area of.

Therefore, the parallelogram has the same area of a rectangle. Thus:

Area of Parallelogram = Base x perpendicular Height Example 1: Find the area of this quadrilateral.

CUT HERE!!

PLACE HERE!!

BASE

HEIGHT



Area of Parallelogram = Base x perpendicular height = 10 6 = 60 cm2 Example 2: Find the area of this quadrilateral.

Area of Parallelogram = Base x perpendicular height = 25 5 = 125 cm2

5.5 Area of a Triangle. Any triangle is half a parallelogram or half a rectangle or half a square.

Base Base Base Area of triangle = half area of parallelogram = half area of rectangle = half area of square Thus:

Area of triangle = 12

(base perpendicular height)

10 cm

6 cm

5 cm

25 cm

Perpendicular Height



Example: Find the areas of these triangles:

a)


(base x perpendicular height)

= 12

(12 6)

= 12

(72)

= 36 cm2

b)



= 12

( 4 7)

= 12

(28)

6 cm

12 cm



= 14 m2

5.6 Area of a Kite (Compound triangles). Find the area of each of these kites by splitting them into triangles. The kite is made up of two triangles: Area of Kite = Area of triangle A + Area of triangle B

= 12

(base perpendicular height) + 12


10 cm

2 cm

5 cm

5 cm

5 cm

2 cm

10cm 2cm = 8cm

A

B



= 12

(5 2) + 12

(5 8)

= 12

(10) + 12

( 40)

= 5 + 20

= 25 cm2

Example 2: Area of Kite = (Area of triangle A) + (Area of triangle B)

= 12

(base perpendicular height) + 12


= 12

(15 5) + 12

(15 15)

= 12

(75) + 12

(225)

= 37.5 + 112.5

= 150 cm2

20 cm

15 cm

5 cm



5.7 Area of Trapezium. We will find the area of a trapezium by spitting it up into shapes. Example 1: Find the area of the following trapezium. We can split this trapezium into a rectangle and a triangle. Area of Trapezium = Area of Rectangle + Area of Triangle = (l b) + 12 (b h)

= (5 6) + 12 (5 5)

= 30 + 12.5

= 42.5 m2



Example 2: Find the area of the following trapezium in cm2. ATTENTION! : Note that not all the measurements are in cm. Convert all measurement to cm before working out the area. (50 mm = 5 cm). We can split this trapezium into two triangles and a rectangle. Area of Trapezium = Area of Rectangle + Area of Triangle + Area of Triangle = (l b) + 12 (b h) +

12 (b h)

= (7 5) + 12 ( 3 5) + 1

2 (3 5) = 35 + 7.5 + 7.5 = 50cm2 5.8 What is volume? Volume and surface area of a Cube/ Cuboid. What is volume? Most everyday objects are three dimensional. Lets try and look around us! Most objects in our everyday life have length, width and height! Volume of a 3-D object is the total space it takes up. We measure volume in mm3, cm3, m3 and km3.

7 cm

50 mm

13 cm

Triangle Triangle Rectangle



Cube A cube is a 3-D shape with all faces equal. All faces are squares.

If we lay the shape out flat (net), we see that the surface of the cube is made up of 6 squares of equal dimensions. The surface area is the area of the net.

Example 1: Draw a cube with dimensions 5cm by 5cm.

a) What is the volume? b) What is the surface area of this cube?

a) Volume = l b h = 5 5 5 = 25 5 = 125 cm3

b) Surface Area = Area of net = 6 (l b) = 6 (5 5) = 6 (25) = 150 cm2

5 cm

5 cm 5 cm

Volume = Length Breadth Height

5 cm

5 cm

5 cm



Cuboid

Example 2: Draw a cuboid with dimensions 5 cm by 6 cm by 7 cm.

a) What is its volume? b) Find the surface area of this cuboid.

a) Volume of cuboid = l x b x h = 7 x 6 x 5 = 210 cm3

b) Surface Area = Area of each face of the net

(1) and (3) = 5 x 7 = 35 cm2 (2) and (4) = 7 x 6 = 42 cm2 (5) and (6) = 5 x 6 = 30 cm2

Add the areas up: The surface area is 214 cm2

35 x 2 = 70 42 x 2 = 84 30 x 2 = 60 +

214 cm2

The opposite faces are equal sized rectangles.

Volume = Length Breadth Height

The net of a cuboid

7 cm 5 cm

6 cm

7 cm

5 cm

6 cm

(1)

(2)

(3)

(4)

(5) (6)

FORM 1 Chapter 5 Perimeter, Area and Volume 2014

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Transcript of FORM 1 Chapter 5 Perimeter, Area and Volume 2014