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 : 4 respectively. Given that half of the area of P is shaded and the total area of all the shaded parts is 80 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 |
|
|
4 |
|
1x3 |
1x3 |
|
|
|
|
3 u |
3 u |
7 u |
5 u |
4 u |
2 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 : 4
Total shaded area
= 3 u + 2 u
= 5 u
5 u = 80
1 u = 80 ÷ 5 = 16
Area of the whole figure
= 3 u + 12 u + 4 u
= 19 u
= 19 x 16
= 304 cm
2 Answer(s): 304 m
2