The figure, not drawn to scale, shows a rectangle, CDEF, which is divided in 4 parts, G, H, J, and K. The ratio of the area of K to the area of J is 1 : 3. The ratio of the area of J to the area of H is 7 : 9. If the area of G is 234 cm
2, what is the area of the rectangle CDEF?
K |
J |
H |
G |
1x7 |
3x7 |
|
|
|
7x3 |
9x3 |
|
7 u |
21 u |
27 u |
13 u |
Area J is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area K + Area H
= 7 u + 27 u
= 34 u
Area of G
= Half of the area of the rectangle - Area J
= 34 u - 21 u
= 13 u
13 u = 234
1 u = 234 ÷ 13 = 18
Area of the rectangle
= 34 u x 2
= 68 u
= 68 x 18
= 1224 cm
2 Answer(s): 1224 cm
2