The figure, not drawn to scale, is made up of two identical squares, L and N and a rectangle M. The ratio of the area L to the area of M to the area of N is 1 : 2 : 1. The ratio of the unshaded part of L to the unshaded part of N is 3 : 5 respectively. Given that half of the area of L is shaded and the total area of all the shaded parts is 72 cm², what is the area of the whole figure?

L		M		N
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 L is shaded, the other half of the area of L is unshaded.
Unshaded part of L : Shaded part of L
1 : 1

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

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

L : M : N
1 : 2 : 1
6 : 12 : 6

Shaded part of L : Shaded part of N
3 : 5

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

4 u = 72

1 u = 72 ÷ 4 = 18

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 18 
= 360 cm²

Answer(s): 360 m²