Question

In the given figure, $ABED$ is a parallelogram in which $AB=DE=10cm$ and the area of $△BEC$ is $72c{m}^2$. If $CE=16cm$, find the area of the trapezium $ABCD$

Answer 1

Area of $△BEC=\times Base\times altitude$
$72=\frac{1}{2}\times 16\times h$
$h=\frac{72\times 2}{16}=9cm$
In trapezium $ABCD$
$AB=10cm$
$DC=DE+EC(\because DE=AB)$
$=10cm+16cm=26cm$
$\therefore$ Area of the trapezium $ABCD$
$=\frac{1}{2}\times (a+b)\times h$
$=\frac{1}{2}(AB+DC)h$
$=\frac{1}{2}(10+26)\times 9c{m}^2$
$=18\times 9c{m}^2$
$=162c{m}^2$