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 : 2. The ratio of the area of G to the area of F is 7 : 9. If the area of E is 275 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
1x7 |
2x7 |
|
|
|
7x2 |
9x2 |
|
7 u |
14 u |
18 u |
11 u |
Area G is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area H + Area F
= 7 u + 18 u
= 25 u
Area of E
= Half of the area of the rectangle - Area G
= 25 u - 14 u
= 11 u
11 u = 275
1 u = 275 ÷ 11 = 25
Area of the rectangle
= 25 u x 2
= 50 u
= 50 x 25
= 1250 cm
2 Answer(s): 1250 cm
2