Question

A field is in the shape of a trapezium whose parallel sides are $25m$ and $10m$. The non-parallel sides are $14m$ and $13m$. Find the area of the field.

• A. $220$ sq m
• B. $192$ sq m
• C. $186$ sq m
• D. $196$ sq m

Answer 1

The correct option is D $196$ sq m

Area of field $ABCD=arABED+ar△BEC$

$ar△BEC=\sqrt{s(s-a)(s-b)(s-c)},S=\frac{13+14+15}{2}=21m$

$\Rightarrow =\sqrt{21(21-13)(21-14)(21-15)}=\sqrt{21\times 8\times 7\times 6}$

$ar△BEC=84m^2$

$\Rightarrow \frac{1}{2}\times 15\times BF=84m^2\Rightarrow BF=\frac{84\times 2}{15}=11.2m$

$\therefore arABED=base\times altitude=10\times 11.2=112m^2$

$\Rightarrow arABCD=112+84=196m^2$