Question

A pond is in the shape of a trapezoid. A bridge that is perpendicular to the parallel sides of the pond has to be constructed. If the area of the pond is 1586 $m^2$ and if the lengths of its parallel sides are 84 m and 38 m, then find the length of the bridge.

Answer 1

Given:
Area of the pond = 1586 m${}^2$
The lengths of the parallel sides are 84 m and 38 m.



Let the length of the bridge be '$x$' m.

$\because$ Area of a trapezoid
$=\frac{1}{2}\times \text{(Sum of parallel sides)}\times \text{Perpendicular distance between them}$

$\Rightarrow 1586=\frac{1}{2}\times (84+38)\times x\Rightarrow x=\frac{1586\times 2}{84+38}$
$=\frac{3172}{112}=26$

$\therefore$ The length of the bridge is 26 m.