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 2 : 5. The ratio of the area of G to the area of F is 8 : 9. If the area of E is 315 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
2x8 |
5x8 |
|
|
|
8x5 |
9x5 |
|
16 u |
40 u |
45 u |
21 u |
Area G is the repeated identity.
LCM of 5 and 8 = 40
Half of the area of the rectangle
= Area H + Area F
= 16 u + 45 u
= 61 u
Area of E
= Half of the area of the rectangle - Area G
= 61 u - 40 u
= 21 u
21 u = 315
1 u = 315 ÷ 21 = 15
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 15
= 1830 cm
2 Answer(s): 1830 cm
2