Question

The parallel sides of a trapezium are $20m$ and $30m$ and its non parallel sides are $6m$ and $8m$. Find the area of the trapezium.

• A. $96$ $m^2$
• B. $82$ $m^2$
• C. $100$ $m^2$
• D. $120$ $m^2$

Answer 1

The correct option is A $96$ $m^2$

Draw $BE\parallel AD$, then $AB\parallel DE$

Hence $ABED$ is a parallelogram

$\therefore AB=DE=20m$

$AD=BE=8m$

$EC=DC-DE=30-20=10m$

Now, using Heron's formula,

$ar△BCE=\sqrt{s(s-a)(s-b)(s-c)}$ where $,s=\frac{8+6+10}{2}=12m$

$\therefore ar△BCE=\sqrt{12(12-8)(12-6)(12-10)}$

$=\sqrt{12\times 4\times 6\times 2}$

$=2\times 12=24m^2$

Also, $ar△BCE$,

$\frac{1}{2}\times EC\times BF=24m^2$

$\Rightarrow BF=\frac{24\times 2}{10}=4.8m$

$\therefore arABCD=\frac{1}{2}\times (AB+CD)\times BF=\frac{1}{2}\times (20+30)\times 4.8$

$=50\times 2.4$

$=120m^2$