The figure, not drawn to scale, shows a rectangle, MNPQ, which is divided in 4 parts, R, S, T, and U. The ratio of the area of U to the area of T is 2 : 5. The ratio of the area of T to the area of S is 7 : 8. If the area of R is 532 cm
2, what is the area of the rectangle MNPQ?
| U |
T |
S |
R |
| 2x7 |
5x7 |
|
|
| |
7x5 |
8x5 |
|
| 14 u |
35 u |
40 u |
19 u |
Area T is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area U + Area S
= 14 u + 40 u
= 54 u
Area of R
= Half of the area of the rectangle - Area T
= 54 u - 35 u
= 19 u
19 u = 532
1 u = 532 ÷ 19 = 28
Area of the rectangle
= 54 u x 2
= 108 u
= 108 x 28
= 3024 cm
2 Answer(s): 3024 cm
2 
