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 : 3. The ratio of the area of U to the area of T is 7 : 9. If the area of S is 260 cm
2, what is the area of the rectangle NPQR?
V |
U |
T |
S |
1x7 |
3x7 |
|
|
|
7x3 |
9x3 |
|
7 u |
21 u |
27 u |
13 u |
Area U is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area V + Area T
= 7 u + 27 u
= 34 u
Area of S
= Half of the area of the rectangle - Area U
= 34 u - 21 u
= 13 u
13 u = 260
1 u = 260 ÷ 13 = 20
Area of the rectangle
= 34 u x 2
= 68 u
= 68 x 20
= 1360 cm
2 Answer(s): 1360 cm
2