1. Composite Areas Teacher Extraordinaire will
Mr. Peter Richard
Teacher Extraordinaire will
Show you how to compose yourself!
Area of a rectangle
Area of a triangle
Area of Circles
Area of composite shapes

2. Solution.
Example 3.
8cm
2cm
5cm
3cm
Split the shape up into two rectangles: A1
Calculate the area of A1 and A2. A2 2 A1 A2 3 5 6
Calculate the area of the shape above:
Area = A1 + A2
Area = ( 2 x 5) + (6 x 3)
Area =
Area = 28cm2

3. Example 3.
Calculate the area of the shape below:
Solution.
16m
12m
10m
Divide the shape into parts: A1 A2
Area = A1 + A2 A1 A2 10 10 12
16-12 =4
Area = LB + 1/2 BH
Area = 10 x ½ x 4 x 10
Area =
Area = 140m2

4. We are now going to find a formula for the area of the trapezium:b h
Area = A1 + ( A2 + A3 )
Area = b x h + ½ x (a - b) x h
Area = bh + ½ h(a - b)
Divide the shape into parts:
Area = bh + ½ ah – ½ bh A2 A1 A3
Area = ½ ah + ½ bh
Work out the dimensions of the shapes:
Area = ½ h ( a + b ) b A2 A3 A1 h
Often common sense is as good as the formula to work out the area of a trapezium. h
a – b

5. Example 2
Divide the shape into parts: 8m
14m
10m
Area = rectangle + triangle
Area = LB + ½ B H
A = ( 10 x 8 ) + ( ½ x 6 x 10 )
A =
A = 110 m 2 10 10
14 – 8 = 6 8

6. Composite shapes
10 cm
6 cm ? ?
3 cm
13 cm

7. Composite shapes Area (1) = l x w = 10 x 6 = 60 cm² Area (2)?
(2)
3 cm
Area (1)
= l x w
= 10 x 6
= 60 cm²
Area (2)
= ½ x b x h
= ½ x 3 x 6
= 9 cm²
Area of shape
= (1) + (2) =
= 69 cm²

8. Example 4
Example 3
12cm
7cm A1 A2
7cm
Split the shape into two areas.
Find half the area of a circle:
Area = A1 + A2
A =  r 2 2
Area = LB + ½  r 2.
L = 12
B = 7
r = 3.5
A = 3.14 x 7 x 7 2
A = 12 x 7 + ½ x 3.14 x 3.5 x 3.5
A =
A = 76.93cm2
A = 103.2cm 2. (to 1 d.p)

9. Composite shapes Quiz and Homework! Quiz: Worksheet Page 249
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