The figure, not drawn to scale, is made up of two identical squares, G and J and a rectangle H. The ratio of the area G to the area of H to the area of J is 1 : 2 : 1. The ratio of the unshaded part of G to the unshaded part of J is 3 : 5 respectively. Given that half of the area of G is shaded and the total area of all the shaded parts is 48 cm², what is the area of the whole figure?

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

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

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

G : H : J
1 : 2 : 1
6 : 12 : 6

Shaded part of G : Shaded part of J
3 : 5

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

4 u = 48

1 u = 48 ÷ 4 = 12

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 12 
= 240 cm²

Answer(s): 240 m²