The figure, not drawn to scale, is made up of two identical squares, V and X and a rectangle W. The ratio of the area V to the area of W to the area of X is 1 : 2 : 1. The ratio of the unshaded part of V to the unshaded part of X is 3 : 4 respectively. Given that half of the area of V is shaded and the total area of all the shaded parts is 90 cm², what is the area of the whole figure?

V		W		X
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 V is shaded, the other half of the area of V is unshaded.
Unshaded part of V : Shaded part of V
1 : 1

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

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

V : W : X
1 : 2 : 1
6 : 12 : 6

Shaded part of V : Shaded part of X
3 : 4

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

5 u = 90

1 u = 90 ÷ 5 = 18

Area of the whole figure
= 3 u + 12 u + 4 u
= 19 u
= 19 x 18 
= 342 cm²

Answer(s): 342 cm²