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 6 : 7. If the area of E is 36 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
1x2 |
3x2 |
|
|
|
6x1 |
7x1 |
|
2 u |
6 u |
7 u |
3 u |
Area G is the repeated identity.
LCM of 3 and 6 = 6
Half of the area of the rectangle
= Area H + Area F
= 2 u + 7 u
= 9 u
Area of E
= Half of the area of the rectangle - Area G
= 9 u - 6 u
= 3 u
3 u = 36
1 u = 36 ÷ 3 = 12
Area of the rectangle
= 9 u x 2
= 18 u
= 18 x 12
= 216 cm
2 Answer(s): 216 cm
2