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 7 : 8. If the area of S is 220 cm
2, what is the area of the rectangle NPQR?
V |
U |
T |
S |
1x7 |
4x7 |
|
|
|
7x4 |
8x4 |
|
7 u |
28 u |
32 u |
11 u |
Area U is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area V + Area T
= 7 u + 32 u
= 39 u
Area of S
= Half of the area of the rectangle - Area U
= 39 u - 28 u
= 11 u
11 u = 220
1 u = 220 ÷ 11 = 20
Area of the rectangle
= 39 u x 2
= 78 u
= 78 x 20
= 1560 cm
2 Answer(s): 1560 cm
2