The figure, not drawn to scale, is made up of two identical squares, Y and A and a rectangle Z. The ratio of the area Y to the area of Z to the area of A is 1 : 2 : 1. The ratio of the unshaded part of Y to the unshaded part of A is 3 : 5 respectively. Given that half of the area of Y is shaded and the total area of all the shaded parts is 32 cm², what is the area of the whole figure?

Y		Z		A
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 Y is shaded, the other half of the area of Y is unshaded.
Unshaded part of Y : Shaded part of Y
1 : 1

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

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

Y : Z : A
1 : 2 : 1
6 : 12 : 6

Shaded part of Y : Shaded part of A
3 : 5

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

4 u = 32

1 u = 32 ÷ 4 = 8

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 8 
= 160 cm²

Answer(s): 160 cm²