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 : 4. The ratio of the area of T to the area of S is 9 : 10. If the area of R is 156 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x9 |
4x9 |
|
|
|
9x4 |
10x4 |
|
9 u |
36 u |
40 u |
13 u |
Area T is the repeated identity.
LCM of 4 and 9 = 36
Half of the area of the rectangle
= Area U + Area S
= 9 u + 40 u
= 49 u
Area of R
= Half of the area of the rectangle - Area T
= 49 u - 36 u
= 13 u
13 u = 156
1 u = 156 ÷ 13 = 12
Area of the rectangle
= 49 u x 2
= 98 u
= 98 x 12
= 1176 cm
2 Answer(s): 1176 cm
2