The figure, not drawn to scale, is made up of two identical squares, N and Q and a rectangle P. The ratio of the area N to the area of P to the area of Q is 1 : 2 : 1. The ratio of the unshaded part of N to the unshaded part of Q is 2 : 3 respectively. Given that half of the area of N is shaded and the total area of all the shaded parts is 24 cm
2, what is the area of the whole figure?
N |
P |
Q |
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 N is shaded, the other half of the area of N is unshaded.
Unshaded part of N : Shaded part of N
1 : 1
The unshaded part of N is the repeated identity.
LCM of 1 and 2 = 2
Area of N is the combined repeated identity.
LCM of 1 and 4 = 4
N : P : Q
1 : 2 : 1
4 : 8 : 4
Shaded part of N : Shaded part of Q
2 : 3
Total shaded area
= 2 u + 1 u
= 3 u
3 u = 24
1 u = 24 ÷ 3 = 8
Area of the whole figure
= 2 u + 8 u + 3 u
= 13 u
= 13 x 8
= 104 cm
2 Answer(s): 104 m
2