The figure, not drawn to scale, shows a rectangle, STUV, which is divided in 4 parts, W, X, Y, and Z. The ratio of the area of Z to the area of Y is 1 : 4. The ratio of the area of Y to the area of X is 7 : 8. If the area of W is 231 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
1x7 |
4x7 |
|
|
|
7x4 |
8x4 |
|
7 u |
28 u |
32 u |
11 u |
Area Y is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area Z + Area X
= 7 u + 32 u
= 39 u
Area of W
= Half of the area of the rectangle - Area Y
= 39 u - 28 u
= 11 u
11 u = 231
1 u = 231 ÷ 11 = 21
Area of the rectangle
= 39 u x 2
= 78 u
= 78 x 21
= 1638 cm
2 Answer(s): 1638 cm
2