The figure, not drawn to scale, shows a rectangle, GHJK, which is divided in 4 parts, L, M, N, and P. The ratio of the area of P to the area of N is 1 : 4. The ratio of the area of N to the area of M is 8 : 9. If the area of L is 69 cm
2, what is the area of the rectangle GHJK?
| P |
N |
M |
L |
| 1x2 |
4x2 |
|
|
| |
8x1 |
9x1 |
|
| 2 u |
8 u |
9 u |
3 u |
Area N is the repeated identity.
LCM of 4 and 8 = 8
Half of the area of the rectangle
= Area P + Area M
= 2 u + 9 u
= 11 u
Area of L
= Half of the area of the rectangle - Area N
= 11 u - 8 u
= 3 u
3 u = 69
1 u = 69 ÷ 3 = 23
Area of the rectangle
= 11 u x 2
= 22 u
= 22 x 23
= 506 cm
2 Answer(s): 506 cm
2 
