The figure, not drawn to scale, is made up of two identical squares, Q and S and a rectangle R. The ratio of the area Q to the area of R to the area of S is 1 : 2 : 1. The ratio of the unshaded part of Q to the unshaded part of S is 3 : 5 respectively. Given that half of the area of Q is shaded and the total area of all the shaded parts is 20 cm², what is the area of the whole figure?

Q		R		S
1x6 = 6 u		2x6 = 12 u		1x6 = 6 u
Unshaded	Shaded	Unshaded	Shaded	Unshaded	Shaded
	3			5
1x3	1x3
3 u	3 u	8 u	4 u	5 u	1 u

Since half of the area of Q is shaded, the other half of the area of Q is unshaded.
Unshaded part of Q : Shaded part of Q
1 : 1

The unshaded part of Q is the repeated identity.
LCM of 1 and 3 = 3

Area of Q is the combined repeated identity.
LCM of 1 and 6 = 6

Q : R : S
1 : 2 : 1
6 : 12 : 6

Shaded part of Q : Shaded part of S
3 : 5

Total shaded area
= 3 u + 1 u
= 4 u

4 u = 20

1 u = 20 ÷ 4 = 5

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 5 
= 100 cm²

Answer(s): 100 m²