The figure, not drawn to scale, shows a rectangle, KLMN, which is divided in 4 parts, P, Q, R, and S. The ratio of the area of S to the area of R is 2 : 7. The ratio of the area of R to the area of Q is 4 : 5. If the area of P is 270 cm
2, what is the area of the rectangle KLMN?
| S |
R |
Q |
P |
| 2x4 |
7x4 |
|
|
| |
4x7 |
5x7 |
|
| 8 u |
28 u |
35 u |
15 u |
Area R is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area S + Area Q
= 8 u + 35 u
= 43 u
Area of P
= Half of the area of the rectangle - Area R
= 43 u - 28 u
= 15 u
15 u = 270
1 u = 270 ÷ 15 = 18
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 18
= 1548 cm
2 Answer(s): 1548 cm
2 
