Question

The diagonal of a quadrilateral shaped field is $24m$ and the perpendiculars dropped on it from the remaining opposite vertices are $8m$ and $13m$. Find the area of the field.

Answer 1

Given: Diagonal of a quadrilateral shaped field $=24m$
Perpendiculars dropped on it from the remaining opposite vertices are
$h_1=8m$ and $h_2=13m$.
Now, we know: Area $=\frac{1}{2}\times d\times (h_1+h_2)$
Thus, Area of the field$=\frac{1}{2}\times 24\times (8+13)$
$=12\times 21$
$=252m^2$
Therefore, the area of the quadrilateral is $252m^2$.