The figure, not drawn to scale, is made up of two identical squares, B and D and a rectangle C. The ratio of the area B to the area of C to the area of D is 1 : 2 : 1. The ratio of the unshaded part of B to the unshaded part of D is 3 : 5 respectively. Given that half of the area of B is shaded and the total area of all the shaded parts is 64 cm², what is the area of the whole figure?

B		C		D
1x6 = 6 u		2x6 = 12 u		1x6 = 6 u
Unshaded	Shaded	Unshaded	Shaded	Unshaded	Shaded
	3			5
1x3	1x3
3 u	3 u	8 u	4 u	5 u	1 u

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

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

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

B : C : D
1 : 2 : 1
6 : 12 : 6

Shaded part of B : Shaded part of D
3 : 5

Total shaded area
= 3 u + 1 u
= 4 u

4 u = 64

1 u = 64 ÷ 4 = 16

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 16 
= 320 cm²

Answer(s): 320 m²