Question

A quadrilateral has an area of 453.6 $c{m}^2$. The length of a diagonal is 42 cm and the perpendicular distance from one vertex is 10 cm. Find the perpendicular distance from the other vertex (in cm). ___​

Answer 1

Area of a quadrilateral can be written as the sum of two triangles.


Let the perpendicular distance from the other vetex be x
Therefore, area of field = Ar of $\Delta$ ADC + Ar of $\Delta$ ABC
$\Rightarrow$ 453.6$c{m}^2$ = $\frac{1}{2}$ $\times$ 42 $\times$ 10 + $\frac{1}{2}$ $\times$ 42 $\times$ $x$
$\Rightarrow$ x = 11.6 cm