Question

Calculate the area of a quadrilateral $ABCD$ when the length of the diagonal $AC=10cm$ and the lengths of perpendiculars from $B$and $D$ on $AC$ be $5cm$ and $6cm$ respectively.

Answer 1

Length of the diagonal $AC=10cm$

Area of quadrilateral

$\begin{array}{rcl}ABCD& =& ar\left(∆ABC\right)+ar\left(∆ACD\right)\\ & =& \left(\frac{1}{2}\times AC\times BH\right)+\left(\frac{1}{2}\times AC\times DL\right)\\ & =& \frac{1}{2}\times AC\left(BM+DL\right)\\ & =& \frac{1}{2}\times 10\times \left(5+6\right)\\ & =& 5\times 11c{m}^2\\ & =& 55c{m}^2\end{array}$

Hence, the required value is $55c{m}^2$.