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 2 : 3 respectively. Given that half of the area of G is shaded and the total area of all the shaded parts is 15 cm
2, what is the area of the whole figure?
G |
H |
J |
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 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 2 = 2
Area of G is the combined repeated identity.
LCM of 1 and 4 = 4
G : H : J
1 : 2 : 1
4 : 8 : 4
Shaded part of G : Shaded part of J
2 : 3
Total shaded area
= 2 u + 1 u
= 3 u
3 u = 15
1 u = 15 ÷ 3 = 5
Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 5
= 65 cm
2 Answer(s): 65 m
2