The figure, not drawn to scale, is made up of two identical squares, J and L and a rectangle K. The ratio of the area J to the area of K to the area of L is 1 : 2 : 1. The ratio of the unshaded part of J to the unshaded part of L is 3 : 5 respectively. Given that half of the area of J is shaded and the total area of all the shaded parts is 60 cm², what is the area of the whole figure?

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

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

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

J : K : L
1 : 2 : 1
6 : 12 : 6

Shaded part of J : Shaded part of L
3 : 5

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

4 u = 60

1 u = 60 ÷ 4 = 15

Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 15 
= 300 cm²

Answer(s): 300 m²