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 : 2. The ratio of the area of U to the area of T is 6 : 7. If the area of S is 108 cm
2, what is the area of the rectangle NPQR?
V |
U |
T |
S |
1x3 |
2x3 |
|
|
|
6x1 |
7x1 |
|
3 u |
6 u |
7 u |
4 u |
Area U is the repeated identity.
LCM of 2 and 6 = 6
Half of the area of the rectangle
= Area V + Area T
= 3 u + 7 u
= 10 u
Area of S
= Half of the area of the rectangle - Area U
= 10 u - 6 u
= 4 u
4 u = 108
1 u = 108 ÷ 4 = 27
Area of the rectangle
= 10 u x 2
= 20 u
= 20 x 27
= 540 cm
2 Answer(s): 540 cm
2