The figure, not drawn to scale, is made up of two identical squares, T and V and a rectangle U. The ratio of the area T to the area of U to the area of V is 1 : 2 : 1. The ratio of the unshaded part of T to the unshaded part of V is 3 : 5 respectively. Given that half of the area of T is shaded and the total area of all the shaded parts is 52 cm², what is the area of the whole figure?

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

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

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

T : U : V
1 : 2 : 1
6 : 12 : 6

Shaded part of T : Shaded part of V
3 : 5

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

4 u = 52

1 u = 52 ÷ 4 = 13

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 13 
= 260 cm²

Answer(s): 260 cm²