Question

If the area of the trapezium is 312 $c{m}^2$ then the distance between the parallel sides whose lengths are 21 cm and 27 cm respectively is:

• A. 13 cm
• B. 14 cm
• C. 15 cm
• D. 16 cm

Answer 1

Answer: (A)

13 cm

Given: The area of trapezium is $312c{m}^2$ and the length of two parallel sides are $21cm$ and $27cm$.

We know that the area of trapezium $=\frac{1}{2}\times \left(\text{sum of parallel sides}\right)\left(\text{Distance between parallel sides}\right)$

$=\frac{1}{2}(21+27)x$ (where $x$ is the distance between parallel sides)

But given the area $=312c{m}^2$

$\therefore \frac{1}{2}(27+21)x=312$

$\Rightarrow 24x=312$

$\Rightarrow x=13$ cm

Therefore, the distance between parallel sides $=13cm$.