Question

Find the area of a quadrilateral one of whose diagonals is $40cm$ and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are $16cm$ and $12cm$.

Answer 1

Let $ABCD$ be a quadilateral.

Diagonal, $AC=40cm$, $BL\perp AC$, such that $BL=16cm$

$DM\perp AC$, such that $DM=12cm$

Area of the quadrilateral $ABCD=$ Area of $\Delta DAC$ + Area of $\Delta ACB$
$=(\frac{1}{2}\times AC\times DM)+(\frac{1}{2}\times AC\times BLc{m}^2)$

$=\frac{1}{2}\times 40\times 12+\frac{1}{2}\times 40\times 16c{m}^2$

$=240+320c{m}^2=560c{m}^2$
Hence, the area of the quadrilateral $ABCD$ is $560c{m}^2$.