The figure, not drawn to scale, is made up of two identical squares, Z and B and a rectangle A. The ratio of the area Z to the area of A to the area of B is 1 : 2 : 1. The ratio of the unshaded part of Z to the unshaded part of B is 3 : 4 respectively. Given that half of the area of Z is shaded and the total area of all the shaded parts is 40 cm², what is the area of the whole figure?

Z		A		B
1x6 = 6 u		2x6 = 12 u		1x6 = 6 u
Unshaded	Shaded	Unshaded	Shaded	Unshaded	Shaded
	3			4
1x3	1x3
3 u	3 u	7 u	5 u	4 u	2 u

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

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

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

Z : A : B
1 : 2 : 1
6 : 12 : 6

Shaded part of Z : Shaded part of B
3 : 4

Total shaded area
= 3 u + 2 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Area of the whole figure
= 3 u + 12 u + 4 u
= 19 u
= 19 x 8 
= 152 cm²

Answer(s): 152 cm²