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 : 3. The ratio of the area of G to the area of F is 8 : 9. If the area of E is 220 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
1x8 |
3x8 |
|
|
|
8x3 |
9x3 |
|
8 u |
24 u |
27 u |
11 u |
Area G is the repeated identity.
LCM of 3 and 8 = 24
Half of the area of the rectangle
= Area H + Area F
= 8 u + 27 u
= 35 u
Area of E
= Half of the area of the rectangle - Area G
= 35 u - 24 u
= 11 u
11 u = 220
1 u = 220 ÷ 11 = 20
Area of the rectangle
= 35 u x 2
= 70 u
= 70 x 20
= 1400 cm
2 Answer(s): 1400 cm
2