Question

A field is in the shape of a trapezium whose parallel sides are 25m and 10m.The non-parallel sides are14 m and 13 m. Find the area of the field.

Answer 1

Draw a line BE parallel to AD and draw a perpendicular BF on CD.

It can be observed that ABED is a parallelogram.
BE = AD =13 m and ED = AB = 10 m
Also, EC = 25 −ED = 15 m

For $\Delta BEC$,
Semi-perimeter,
$s=\frac{(13+14+15)}{2}=21m$

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

Area of $\Delta BEC=\lfloor \sqrt{21(21-13)(21-14)(21-15)}\rfloor m^2=\lfloor \sqrt{21\left(8\right)\left(7\right)\left(6\right)}\rfloor =84m^{2}Areaof\Delta BEC=\frac{1}{2}\times CE\times BF84c{m}^2=\frac{1}{2}\times 15cm\times BFBF=\left(\frac{168}{15}\right)cm=11.2cmAreaofABED=BF\times DE=11.2\times 10=112m^{2}Areaofthefield=84+112=196m^2$