The figure, not drawn to scale, is made up of two identical squares, U and W and a rectangle V. The ratio of the area U to the area of V to the area of W is 1 : 2 : 1. The ratio of the unshaded part of U to the unshaded part of W is 2 : 3 respectively. Given that half of the area of U is shaded and the total area of all the shaded parts is 60 cm
2, what is the area of the whole figure?
U |
V |
W |
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 U is shaded, the other half of the area of U is unshaded.
Unshaded part of U : Shaded part of U
1 : 1
The unshaded part of U is the repeated identity.
LCM of 1 and 2 = 2
Area of U is the combined repeated identity.
LCM of 1 and 4 = 4
U : V : W
1 : 2 : 1
4 : 8 : 4
Shaded part of U : Shaded part of W
2 : 3
Total shaded area
= 2 u + 1 u
= 3 u
3 u = 60
1 u = 60 ÷ 3 = 20
Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 20
= 260 cm
2 Answer(s): 260 m
2