The figure, not drawn to scale, is made up of two identical squares, W and Y and a rectangle X. The ratio of the area W to the area of X to the area of Y is 1 : 2 : 1. The ratio of the unshaded part of W to the unshaded part of Y is 2 : 3 respectively. Given that half of the area of W is shaded and the total area of all the shaded parts is 24 cm², what is the area of the whole figure?

W		X		Y
1x4 = 4 u		2x4 = 8 u		1x4 = 4 u
Unshaded	Shaded	Unshaded	Shaded	Unshaded	Shaded
	2			3
1x2	1x2
2 u	2 u	5 u	3 u	3 u	1 u

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

The unshaded part of W is the repeated identity.
LCM of 1 and 2 = 2

Area of W is the combined repeated identity.
LCM of 1 and 4 = 4

W : X : Y
1 : 2 : 1
4 : 8 : 4

Shaded part of W : Shaded part of Y
2 : 3

Total shaded area
= 2 u + 1 u
= 3 u

3 u = 24

1 u = 24 ÷ 3 = 8

Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 8 
= 104 cm²

Answer(s): 104 cm²