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 2 : 5. The ratio of the area of Y to the area of X is 4 : 5. If the area of W is 351 cm
2, what is the area of the rectangle STUV?
| Z |
Y |
X |
W |
| 2x4 |
5x4 |
|
|
| |
4x5 |
5x5 |
|
| 8 u |
20 u |
25 u |
13 u |
Area Y is the repeated identity.
LCM of 5 and 4 = 20
Half of the area of the rectangle
= Area Z + Area X
= 8 u + 25 u
= 33 u
Area of W
= Half of the area of the rectangle - Area Y
= 33 u - 20 u
= 13 u
13 u = 351
1 u = 351 ÷ 13 = 27
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 27
= 1782 cm
2 Answer(s): 1782 cm
2 
