**Question:**

The area of a trapezium is 1586 cm2 and the distance between the parallel sides is 26 cm. If one of the parallel sides is 38 cm, find the other.

**Solution:**

Given:

Area of the trapezium $=1586 \mathrm{~cm}^{2}$

Distance between the parallel sides $=26 \mathrm{~cm}$

And, length of one parallel side $=38 \mathrm{~cm}$

Let us suppose the length of the other side to be $x \mathrm{~cm} .$

Now, area of the trapezium $=\frac{1}{2} \times($ Sum of the parallel sides $) \times($ Distance between the parallel sides $)$

$\Rightarrow 1586=\frac{1}{2} \times(38+\mathrm{x}) \times(26)$

$\Rightarrow 1586=\frac{26}{2} \times(38+\mathrm{x})$

$\Rightarrow 13 \times(38+x)=1586$

$\Rightarrow 38+x=\frac{1586}{13}=122$

$\Rightarrow x=122-38=84 \mathrm{~cm}$

Hence, the length of the other parallel side is $84 \mathrm{~cm}$.