The figure, not drawn to scale, is made up of two identical squares, H and K and a rectangle J. The ratio of the area H to the area of J to the area of K is 1 : 2 : 1. The ratio of the unshaded part of H to the unshaded part of K is 3 : 5 respectively. Given that half of the area of H is shaded and the total area of all the shaded parts is 40 cm
2, what is the area of the whole figure?
H |
J |
K |
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 H is shaded, the other half of the area of H is unshaded.
Unshaded part of H : Shaded part of H
1 : 1
The unshaded part of H is the repeated identity.
LCM of 1 and 3 = 3
Area of H is the combined repeated identity.
LCM of 1 and 6 = 6
H : J : K
1 : 2 : 1
6 : 12 : 6
Shaded part of H : Shaded part of K
3 : 5
Total shaded area
= 3 u + 1 u
= 4 u
4 u = 40
1 u = 40 ÷ 4 = 10
Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 10
= 200 cm
2 Answer(s): 200 m
2