The figure, not drawn to scale, shows a rectangle, BCDE, which is divided in 4 parts, F, G, H, and J. The ratio of the area of J to the area of H is 1 : 4. The ratio of the area of H to the area of G is 9 : 10. If the area of F is 234 cm
2, what is the area of the rectangle BCDE?
J |
H |
G |
F |
1x9 |
4x9 |
|
|
|
9x4 |
10x4 |
|
9 u |
36 u |
40 u |
13 u |
Area H is the repeated identity.
LCM of 4 and 9 = 36
Half of the area of the rectangle
= Area J + Area G
= 9 u + 40 u
= 49 u
Area of F
= Half of the area of the rectangle - Area H
= 49 u - 36 u
= 13 u
13 u = 234
1 u = 234 ÷ 13 = 18
Area of the rectangle
= 49 u x 2
= 98 u
= 98 x 18
= 1764 cm
2 Answer(s): 1764 cm
2