The figure, not drawn to scale, is made up of two identical squares, T and V and a rectangle U. The ratio of the area T to the area of U to the area of V is 1 : 2 : 1. The ratio of the unshaded part of T to the unshaded part of V is 2 : 3 respectively. Given that half of the area of T is shaded and the total area of all the shaded parts is 6 cm
2, what is the area of the whole figure?
T |
U |
V |
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 T is shaded, the other half of the area of T is unshaded.
Unshaded part of T : Shaded part of T
1 : 1
The unshaded part of T is the repeated identity.
LCM of 1 and 2 = 2
Area of T is the combined repeated identity.
LCM of 1 and 4 = 4
T : U : V
1 : 2 : 1
4 : 8 : 4
Shaded part of T : Shaded part of V
2 : 3
Total shaded area
= 2 u + 1 u
= 3 u
3 u = 6
1 u = 6 ÷ 3 = 2
Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 2
= 26 cm
2 Answer(s): 26 cm
2