Question

The length of the fence of a trapezium-shaped field ABCD is 130 m and side AB is perpendicular to each of the parallel sides AD and BC. If BC = 54 m, CD = 19 m and AD = 42 m, find the area of the field.

Answer 1

$\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{side}\mathrm{AB}=\left(130-\left(54+19+42\right)\right)\mathrm{m}$
$=15\mathrm{m}$
$\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{trapezium}-\mathrm{shaped}\mathrm{field}=\left\{\frac{1}{2}\times \left(\mathrm{AD}+\mathrm{BC}\right)\times \mathrm{AB}\right\}$
$$\begin{gathered} =\left\{\frac{1}{2}\times \left(42+54\right)\times 15\right\}{\mathrm{m}}^2 \\ =\left(\frac{1}{2}\times 96\times 15\right){\mathrm{m}}^2 \\ =\left(48\times 15\right){\mathrm{m}}^2 \\ =720{\mathrm{m}}^2 \end{gathered}$$

$\mathrm{Hence},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{field}\mathrm{is}720{\mathrm{m}}^2.$