The figure, not drawn to scale, shows a rectangle, HJKL, which is divided in 4 parts, M, N, P, and Q. The ratio of the area of Q to the area of P is 1 : 4. The ratio of the area of P to the area of N is 5 : 7. If the area of M is 234 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
1x5 |
4x5 |
|
|
|
5x4 |
7x4 |
|
5 u |
20 u |
28 u |
13 u |
Area P is the repeated identity.
LCM of 4 and 5 = 20
Half of the area of the rectangle
= Area Q + Area N
= 5 u + 28 u
= 33 u
Area of M
= Half of the area of the rectangle - Area P
= 33 u - 20 u
= 13 u
13 u = 234
1 u = 234 ÷ 13 = 18
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 18
= 1188 cm
2 Answer(s): 1188 cm
2