Question

Length of the fence of a trapezium shaped field $ABCD$ is $120m$. If $BC=48m,CD=17m$ and $AD=40m$, find the area of this field. Side $AB$ is perpendicular to the parallel sides $AD$ and $BC$.

Answer 1

Given:

In trapezium $ABCD$,

$BC=48m,CD=17m$ and $AD=40m$

Perimeter of trapezium $=120m$

$AB\perp BC$

Length of the fence of trapezium $ABCD=AB+BC+CD+DA$

$\Rightarrow 120m=AB+48m+17m+40m$

$\Rightarrow AB=120m-105m=15m$

Area of the field $ABCD=\frac{1}{2}(AD+BC)\times AB$

$=\frac{1}{2}\times (40m+48m)\times 15m$

$=\frac{1}{2}\times 88m\times 15m$

$=44m\times 15m$

$=660m^2$