The figure, not drawn to scale, is made up of two identical squares, D and F and a rectangle E. The ratio of the area D to the area of E to the area of F is 1 : 2 : 1. The ratio of the unshaded part of D to the unshaded part of F is 2 : 3 respectively. Given that half of the area of D is shaded and the total area of all the shaded parts is 21 cm², what is the area of the whole figure?

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

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

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

D : E : F
1 : 2 : 1
4 : 8 : 4

Shaded part of D : Shaded part of F
2 : 3

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

3 u = 21

1 u = 21 ÷ 3 = 7

Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 7 
= 91 cm²

Answer(s): 91 cm²