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 1 : 2. The ratio of the area of T to the area of S is 9 : 10. If the area of R is 264 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x9 |
2x9 |
|
|
|
9x2 |
10x2 |
|
9 u |
18 u |
20 u |
11 u |
Area T is the repeated identity.
LCM of 2 and 9 = 18
Half of the area of the rectangle
= Area U + Area S
= 9 u + 20 u
= 29 u
Area of R
= Half of the area of the rectangle - Area T
= 29 u - 18 u
= 11 u
11 u = 264
1 u = 264 ÷ 11 = 24
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 24
= 1392 cm
2 Answer(s): 1392 cm
2