Question

Find the area of a quadrilateral $ABCD$ whose diagonal $AC$ is $25cm$ long and the lengths of perpendicular from opposite vertices $B$ and $D$ on $AC$ are $BE=3.6cm$ and $DF=2.4cm$.

Answer 1

Given $AC=25cm,BE=3.6cm,DF=2.4cm$

Area of quadrilateral = area of $△ABC$+ area of $△ACD$

$=(\frac{1}{2}\times AC\times BE)+(\frac{1}{2}\times AC\times DF)$

$=(\frac{1}{2}\times 25\times 3.6)+(\frac{1}{2}\times 25\times 2.4)$

$=\frac{90}{2}+\frac{60}{2}=45+30=75$

$\therefore$ Area of quadrilateral $=75c{m}^2$