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 7 : 8. If the area of W is 180 cm
2, what is the area of the rectangle STUV?
Z |
Y |
X |
W |
1x7 |
3x7 |
|
|
|
7x3 |
8x3 |
|
7 u |
21 u |
24 u |
10 u |
Area Y is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area Z + Area X
= 7 u + 24 u
= 31 u
Area of W
= Half of the area of the rectangle - Area Y
= 31 u - 21 u
= 10 u
10 u = 180
1 u = 180 ÷ 10 = 18
Area of the rectangle
= 31 u x 2
= 62 u
= 62 x 18
= 1116 cm
2 Answer(s): 1116 cm
2