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 : 2. The ratio of the area of Y to the area of X is 6 : 7. If the area of W is 64 cm
2, what is the area of the rectangle STUV?
| Z |
Y |
X |
W |
| 1x3 |
2x3 |
|
|
| |
6x1 |
7x1 |
|
| 3 u |
6 u |
7 u |
4 u |
Area Y is the repeated identity.
LCM of 2 and 6 = 6
Half of the area of the rectangle
= Area Z + Area X
= 3 u + 7 u
= 10 u
Area of W
= Half of the area of the rectangle - Area Y
= 10 u - 6 u
= 4 u
4 u = 64
1 u = 64 ÷ 4 = 16
Area of the rectangle
= 10 u x 2
= 20 u
= 20 x 16
= 320 cm
2 Answer(s): 320 cm
2 
