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 9 : 10. If the area of S is 273 cm
2, what is the area of the rectangle NPQR?
V |
U |
T |
S |
1x9 |
4x9 |
|
|
|
9x4 |
10x4 |
|
9 u |
36 u |
40 u |
13 u |
Area U is the repeated identity.
LCM of 4 and 9 = 36
Half of the area of the rectangle
= Area V + Area T
= 9 u + 40 u
= 49 u
Area of S
= Half of the area of the rectangle - Area U
= 49 u - 36 u
= 13 u
13 u = 273
1 u = 273 ÷ 13 = 21
Area of the rectangle
= 49 u x 2
= 98 u
= 98 x 21
= 2058 cm
2 Answer(s): 2058 cm
2