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 7 : 8. If the area of R is 319 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x7 |
4x7 |
|
|
|
7x4 |
8x4 |
|
7 u |
28 u |
32 u |
11 u |
Area T is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area U + Area S
= 7 u + 32 u
= 39 u
Area of R
= Half of the area of the rectangle - Area T
= 39 u - 28 u
= 11 u
11 u = 319
1 u = 319 ÷ 11 = 29
Area of the rectangle
= 39 u x 2
= 78 u
= 78 x 29
= 2262 cm
2 Answer(s): 2262 cm
2