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 : 3. The ratio of the area of Y to the area of X is 6 : 7. If the area of W is 54 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
1x2 |
3x2 |
|
|
|
6x1 |
7x1 |
|
2 u |
6 u |
7 u |
3 u |
Area Y is the repeated identity.
LCM of 3 and 6 = 6
Half of the area of the rectangle
= Area Z + Area X
= 2 u + 7 u
= 9 u
Area of W
= Half of the area of the rectangle - Area Y
= 9 u - 6 u
= 3 u
3 u = 54
1 u = 54 ÷ 3 = 18
Area of the rectangle
= 9 u x 2
= 18 u
= 18 x 18
= 324 cm
2 Answer(s): 324 cm
2