The figure, not drawn to scale, is made up of two identical squares, F and H and a rectangle G. The ratio of the area F to the area of G to the area of H is 1 : 2 : 1. The ratio of the unshaded part of F to the unshaded part of H is 2 : 3 respectively. Given that half of the area of F is shaded and the total area of all the shaded parts is 54 cm², what is the area of the whole figure?

F		G		H
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 F is shaded, the other half of the area of F is unshaded.
Unshaded part of F : Shaded part of F
1 : 1

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

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

F : G : H
1 : 2 : 1
4 : 8 : 4

Shaded part of F : Shaded part of H
2 : 3

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

3 u = 54

1 u = 54 ÷ 3 = 18

Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 18 
= 234 cm²

Answer(s): 234 cm²