The figure, not drawn to scale, shows a rectangle, DEFG, which is divided in 4 parts, H, J, K, and L. The ratio of the area of L to the area of K is 1 : 4. The ratio of the area of K to the area of J is 9 : 10. If the area of H is 234 cm
2, what is the area of the rectangle DEFG?
L |
K |
J |
H |
1x9 |
4x9 |
|
|
|
9x4 |
10x4 |
|
9 u |
36 u |
40 u |
13 u |
Area K is the repeated identity.
LCM of 4 and 9 = 36
Half of the area of the rectangle
= Area L + Area J
= 9 u + 40 u
= 49 u
Area of H
= Half of the area of the rectangle - Area K
= 49 u - 36 u
= 13 u
13 u = 234
1 u = 234 ÷ 13 = 18
Area of the rectangle
= 49 u x 2
= 98 u
= 98 x 18
= 1764 cm
2 Answer(s): 1764 cm
2