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 3 : 5 respectively. Given that half of the area of U is shaded and the total area of all the shaded parts is 16 cm
2, what is the area of the whole figure?
U |
V |
W |
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 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 3 = 3
Area of U is the combined repeated identity.
LCM of 1 and 6 = 6
U : V : W
1 : 2 : 1
6 : 12 : 6
Shaded part of U : Shaded part of W
3 : 5
Total shaded area
= 3 u + 1 u
= 4 u
4 u = 16
1 u = 16 ÷ 4 = 4
Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 4
= 80 cm
2 Answer(s): 80 m
2