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 7 : 8. If the area of M is 319 cm
2, what is the area of the rectangle HJKL?
Q |
P |
N |
M |
1x7 |
4x7 |
|
|
|
7x4 |
8x4 |
|
7 u |
28 u |
32 u |
11 u |
Area P is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area Q + Area N
= 7 u + 32 u
= 39 u
Area of M
= Half of the area of the rectangle - Area P
= 39 u - 28 u
= 11 u
11 u = 319
1 u = 319 ÷ 11 = 29
Area of the rectangle
= 39 u x 2
= 78 u
= 78 x 29
= 2262 cm
2 Answer(s): 2262 cm
2