The figure, not drawn to scale, shows a rectangle, JKLM, which is divided in 4 parts, N, P, Q, and R. The ratio of the area of R to the area of Q is 1 : 2. The ratio of the area of Q to the area of P is 6 : 7. If the area of N is 72 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
1x3 |
2x3 |
|
|
|
6x1 |
7x1 |
|
3 u |
6 u |
7 u |
4 u |
Area Q is the repeated identity.
LCM of 2 and 6 = 6
Half of the area of the rectangle
= Area R + Area P
= 3 u + 7 u
= 10 u
Area of N
= Half of the area of the rectangle - Area Q
= 10 u - 6 u
= 4 u
4 u = 72
1 u = 72 ÷ 4 = 18
Area of the rectangle
= 10 u x 2
= 20 u
= 20 x 18
= 360 cm
2 Answer(s): 360 cm
2