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 6 : 7. If the area of E is 135 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
1x3 |
4x3 |
|
|
|
6x2 |
7x2 |
|
3 u |
12 u |
14 u |
5 u |
Area G is the repeated identity.
LCM of 4 and 6 = 12
Half of the area of the rectangle
= Area H + Area F
= 3 u + 14 u
= 17 u
Area of E
= Half of the area of the rectangle - Area G
= 17 u - 12 u
= 5 u
5 u = 135
1 u = 135 ÷ 5 = 27
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 27
= 918 cm
2 Answer(s): 918 cm
2