The figure, not drawn to scale, shows a rectangle, NPQR, which is divided in 4 parts, S, T, U, and V. The ratio of the area of V to the area of U is 1 : 4. The ratio of the area of U to the area of T is 8 : 9. If the area of S is 36 cm
2, what is the area of the rectangle NPQR?
V |
U |
T |
S |
1x2 |
4x2 |
|
|
|
8x1 |
9x1 |
|
2 u |
8 u |
9 u |
3 u |
Area U is the repeated identity.
LCM of 4 and 8 = 8
Half of the area of the rectangle
= Area V + Area T
= 2 u + 9 u
= 11 u
Area of S
= Half of the area of the rectangle - Area U
= 11 u - 8 u
= 3 u
3 u = 36
1 u = 36 ÷ 3 = 12
Area of the rectangle
= 11 u x 2
= 22 u
= 22 x 12
= 264 cm
2 Answer(s): 264 cm
2