Question

A pond is in the shape of a trapezium. A bridge is to be constructed such that the bridge is perpendicular to the parallel sides. It is given that the area of a pond is 1080 $m^2$ and the lengths of its parallel sides are 55.6 m and 34.4 m. Find the length of the bridge.

• A. 24 m
• B. 48 m
• C. 56 m
• D. 12 m

Answer 1

The correct option is A 24 m

Let the length of bridge be $x$ metres.


Given,
$a=55.6m,b=34.4m$
$Area=1080m^2$

Area of trapezium
=$\frac{1}{2}(a+b)\times h$,
where $a$ and $b$ are the lengths of the parallel sides and
$h$, the perpendicular distance between them.

$\Rightarrow \frac{1}{2}\times (55.6+34.4)\times x=1080m^2$

$\Rightarrow \frac{1}{2}\times \left(90\right)\times x=1080m^2$

$\Rightarrow 45\times x=1080m^2$

$\Rightarrow x=\frac{1080}{45}=\frac{216}{9}=24m$

Therefore, the length of the bridge is $24m$.