Question

The difference between two parallel sides of a trapezium is 4 cm.The perpendicular distance between them is 19 cm.Find the area of the trapezium and find the length of parallel sides.

Answer 1

Let the two parallel sides of the trapezium be $a$ cm and $b$ cm.

Given that difference between the two parallel sides is 4 and the perpendicular distance$\left(h\right)$ is 19

$\Rightarrow a-b=4⟶\left(1\right)$

We know that Area of Trapezium = $\frac{1}{2}\times (a+b)\times h$

Substituting the values of $h$ we get,

$\frac{1}{2}\times (a+b)\times 19=475$

$\Rightarrow (a+b)=\frac{475\times 2}{19}$

$\Rightarrow a+b=50⟶\left(2\right)$

Adding (1) and (2),

$a-b=4$

$\underset{–}{a+b=50}$

$-2b=-54$

$b=\frac{54}{2}=27$

Putting $b=27$ in $\left(2\right)$ we get

$a+27=50$

$a=50-27=23$

Two parallel sides are $27$ cm and $23$ cm.