Question

Find the area of a trapezium whose parallel sides are $11cm$ and $25cm$ long, and the nonparallel sides are $15cm$ and $13cm$ long.

Answer 1

Here area of trapezium $=$ Area of parallelogram $+$ area of the triangle

Area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ sq units

$s=\frac{14+15+13}{2}=21$

Area of the triangle $=\sqrt{21(21-14)(21-15)(21-13)}$ sq units

$=\sqrt{21\times 7\times 6\times 8}$

$=\sqrt{7056}=84$ sq units

Also the area of triangle $=\frac{1}{2}\times base\times height$

$84=\frac{1}{2}\times 14\times h$

$h=12$ cm
Hence height of parallelogram is also $12cm$
Area of parallelogram $=base\times height$
$=11\times 12=132$ sq cm

$\therefore$ area of trapezium $=$ Area of parallelogram $+$ area of the triangle
Hence area of trapezium $=84+132=216$ sq cm