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 2 : 7. The ratio of the area of U to the area of T is 4 : 5. If the area of S is 255 cm
2, what is the area of the rectangle NPQR?
| V |
U |
T |
S |
| 2x4 |
7x4 |
|
|
| |
4x7 |
5x7 |
|
| 8 u |
28 u |
35 u |
15 u |
Area U is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area V + Area T
= 8 u + 35 u
= 43 u
Area of S
= Half of the area of the rectangle - Area U
= 43 u - 28 u
= 15 u
15 u = 255
1 u = 255 ÷ 15 = 17
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 17
= 1462 cm
2 Answer(s): 1462 cm
2 
