Question

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

Answer 1

Given : Length of the diagonal $\left(AC\right)=10cm$

Area of quadrilateral

$ABCD=\mathrm{ar}\left(△ABC\right)+\mathrm{ar}\left(△ACD\right)$
$$\begin{array}{cc}& =(\frac{1}{2}\times AC\times BM)+(\frac{1}{2}\times AC\times DL)\\ & =\frac{1}{2}\times AC(BM+DL)\\ & =\frac{1}{2}\times 10(5+6)\\ & =5\times 11{cm}^2=55{cm}^2\end{array}$$