Question

Find the length of the parallel sides of a trapezium, which are in the ratio 1:2, if its height is 2 cm and area is 18$c{m}^2$.

• A. 5 cm, 10 cm
• B. 6 cm, 12 cm
• C. 7 cm, 14 cm
• D. 8 cm, 16 cm

Answer 1

The correct option is B 6 cm, 12 cm

Let the length of the parallel sides be y and 2y.
Area = 18 cm${}^2$ , Height = 2 cm
Area of trapezium = $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$Height
18 = $\frac{1}{2}$$\times$(2y+y)$\times$2
$\frac{18\times 2}{2}$ = $\frac{36}{2}$ = 18 = 3y
$⟹$y = 6
Hence length of the parallel sides = y = 6 cm
The length of the other parallel sides = 2y = 2(6) = 12 cm.