The figure, not drawn to scale, shows a rectangle, KLMN, which is divided in 4 parts, P, Q, R, and S. The ratio of the area of S to the area of R is 1 : 4. The ratio of the area of R to the area of Q is 7 : 8. If the area of P is 319 cm
2, what is the area of the rectangle KLMN?
S |
R |
Q |
P |
1x7 |
4x7 |
|
|
|
7x4 |
8x4 |
|
7 u |
28 u |
32 u |
11 u |
Area R is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area S + Area Q
= 7 u + 32 u
= 39 u
Area of P
= Half of the area of the rectangle - Area R
= 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