The figure, not drawn to scale, is made up of two identical squares, S and U and a rectangle T. The ratio of the area S to the area of T to the area of U is 1 : 2 : 1. The ratio of the unshaded part of S to the unshaded part of U is 2 : 3 respectively. Given that half of the area of S is shaded and the total area of all the shaded parts is 30 cm², what is the area of the whole figure?

S		T		U
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 S is shaded, the other half of the area of S is unshaded.
Unshaded part of S : Shaded part of S
1 : 1

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

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

S : T : U
1 : 2 : 1
4 : 8 : 4

Shaded part of S : Shaded part of U
2 : 3

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

3 u = 30

1 u = 30 ÷ 3 = 10

Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 10 
= 130 cm²

Answer(s): 130 m²