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 6 : 7. If the area of G is 66 cm
2, what is the area of the rectangle CDEF?
K |
J |
H |
G |
1x2 |
3x2 |
|
|
|
6x1 |
7x1 |
|
2 u |
6 u |
7 u |
3 u |
Area J is the repeated identity.
LCM of 3 and 6 = 6
Half of the area of the rectangle
= Area K + Area H
= 2 u + 7 u
= 9 u
Area of G
= Half of the area of the rectangle - Area J
= 9 u - 6 u
= 3 u
3 u = 66
1 u = 66 ÷ 3 = 22
Area of the rectangle
= 9 u x 2
= 18 u
= 18 x 22
= 396 cm
2 Answer(s): 396 cm
2