The figure, not drawn to scale, is made up of two identical squares, P and R and a rectangle Q. The ratio of the area P to the area of Q to the area of R is 1 : 2 : 1. The ratio of the unshaded part of P to the unshaded part of R is 3 : 5 respectively. Given that half of the area of P is shaded and the total area of all the shaded parts is 56 cm
2, what is the area of the whole figure?
P |
Q |
R |
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 P is shaded, the other half of the area of P is unshaded.
Unshaded part of P : Shaded part of P
1 : 1
The unshaded part of P is the repeated identity.
LCM of 1 and 3 = 3
Area of P is the combined repeated identity.
LCM of 1 and 6 = 6
P : Q : R
1 : 2 : 1
6 : 12 : 6
Shaded part of P : Shaded part of R
3 : 5
Total shaded area
= 3 u + 1 u
= 4 u
4 u = 56
1 u = 56 ÷ 4 = 14
Area of the whole figure
= 3 u + 12 u + 5 u
= 20 u
= 20 x 14
= 280 cm
2 Answer(s): 280 m
2