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 8 : 9. If the area of R is 81 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x2 |
4x2 |
|
|
|
8x1 |
9x1 |
|
2 u |
8 u |
9 u |
3 u |
Area T is the repeated identity.
LCM of 4 and 8 = 8
Half of the area of the rectangle
= Area U + Area S
= 2 u + 9 u
= 11 u
Area of R
= Half of the area of the rectangle - Area T
= 11 u - 8 u
= 3 u
3 u = 81
1 u = 81 ÷ 3 = 27
Area of the rectangle
= 11 u x 2
= 22 u
= 22 x 27
= 594 cm
2 Answer(s): 594 cm
2