area - revision

Area - Revision

The area of a shape is simply defined by :

“the amount of space a shape takes up.”

Think of a square measuring 1 cm by 1cm we say it is :

1cm

1cm

1cm2( 1 square centimetre )

Area of a RectangleExampleFind the area of the rectangle

L = 9cm

B = 2cm

Area = Length x BreadthA = L x BA = 9 x 2A = 18 cm2

Area of a Rectangle

ExampleFind the length B of the rectangle opposite

L = 12cm

B cm

Area = Length x BreadthA = L x B

36 = 12 x B

Balancing Method

A = 36cm2

36B = 12B = 3cm

Remember units

Calculate the area of this shape

8cm

9cm

5cm

6cmA = l x bA = 9 x 8A = 72cm2

A = l x bA = 6 x 5A = 30cm2

Total Area == 102cm2

72 + 30

Area of a Composite

Calculate the area of this shape

5cm

6cm

16cm

5cmA = l x bA = 16 x 5A = 80cm2

Rectangle 1

Rectangle 2A = l x bA = 6 x 5 A = 30cm2

Total Area = 80 + 30 =110cm2

Area of a Composite

6

Any Triangle Area

12Area b h

h

b

Sometimes called

the altitude

h = vertical height

7

Any Triangle Area

2

1 8 6224

Area

Area cm

6cm

8cm

Example 1 : Find the area of the triangle.

12Area b h

Any Triangle Area

1 4 102Area 10cm

4cm

Example 2 : Find the area of the triangle.

12Area b hAltitude h outside triangle this time.

220Area cm

Parallelogram Area

b

Parallelogram Area b h

Important NOTE

h = vertical heighth

Parallelogram AreaExample 1 : Find the area of parallelogram.

Parallelogram Area b h Area = 9 3

2Area = 27cm9cm

3cm

Area of a Rhombus

1Rhombus Area= (D×d)2

D

d

Rectangle Area = (D×d)

This part ofthe rhombus

is half of the smallrectangle.

Area of a Kite

1Kite Area= (D×d)2

D

d

Rectangle Area = (D×d)

Exactly the same process as the rhombus

Rhombus and Kite Area

1Rhombus Area= (D×d)21Area = (5×2)2

Example 1 : Find the area of the shapes.

5cm2cm

2Area = 5cm

1Kite Area= (D×d)21Area = (9×4)2

2Area = 18cm

9cm

4cm

Trapezium Area

1Area 1 = a×2 h 1Area 2 = b×2 h1 1Total Area = a× b×2 + 2h h

W

X Y

Z

1

2

a cm

b cm

h cm

Two triangles WXY and WYZ

1Trapezium Area = (a+b)2 h

Trapezium Area

1Trapezium Area = (5+6)×42

1Trapezium Area = (a+b)2 h

Example 1 : Find the area of the trapezium.

6cm

4cm

5cm

2Trapezium Area = 22cm

Parts of the CircleCircumference

O

O = centre of circle

The radius is measured fromthe centre of the circle

to the edge.

radius

diameter

The diameter is measured from one edge to the other

passing through the centre of the circle.Radius = ½ x diameterDiameter = 2 x radius

Circle InvestigationTo calculate the circumference of a circle

C D C circumference

D diameter3.14

Main part of a Circle

10cm

2cm

C D2D r 4D cm

Example : Find the length of the circumference (Perimeter) of each circle

C D 1031.4 cm

412.56 cm

Area of a Circle

To find the area of a circle

A = Πr²

Where A = area r = radius

Area of a circle

Q. Find the area of the circle ?Solution

2A r 24A

250.26A cm

4cm

Area of a circle

Q. The diameter of the circle is 60cm. Find area of the circle?

Solution

2A r60 302 2

Dr cm

230A22826 A cm

What have we learned so farCircumference D

2Area r

Area of a Circle