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 $ABCD=ar\left(△ABC\right)+ar\left(△ACD\right)$

$=(\frac{1}{2}\times AC\times BM)+(\frac{1}{2}\times AC\times DL)$

$=\frac{1}{2}\times AC(BM+DL)$

$=\frac{1}{2}\times 10(5+6)$

$=5\times 11c{m}^2=55c{m}^2$