The figure, not drawn to scale, shows a rectangle, ABCD, which is divided in 4 parts, E, F, G, and H. The ratio of the area of H to the area of G is 1 : 4. The ratio of the area of G to the area of F is 5 : 6. If the area of E is 243 cm
2, what is the area of the rectangle ABCD?
| H |
G |
F |
E |
| 1x5 |
4x5 |
|
|
| |
5x4 |
6x4 |
|
| 5 u |
20 u |
24 u |
9 u |
Area G is the repeated identity.
LCM of 4 and 5 = 20
Half of the area of the rectangle
= Area H + Area F
= 5 u + 24 u
= 29 u
Area of E
= Half of the area of the rectangle - Area G
= 29 u - 20 u
= 9 u
9 u = 243
1 u = 243 ÷ 9 = 27
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 27
= 1566 cm
2 Answer(s): 1566 cm
2 
