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 5 : 6. If the area of W is 261 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
1x5 |
4x5 |
|
|
|
5x4 |
6x4 |
|
5 u |
20 u |
24 u |
9 u |
Area Y is the repeated identity.
LCM of 4 and 5 = 20
Half of the area of the rectangle
= Area Z + Area X
= 5 u + 24 u
= 29 u
Area of W
= Half of the area of the rectangle - Area Y
= 29 u - 20 u
= 9 u
9 u = 261
1 u = 261 ÷ 9 = 29
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 29
= 1682 cm
2 Answer(s): 1682 cm
2