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).

• A. 11.6
• B. 15
• C. 22.5
• D. 12.6

Answer 1

The correct option is A 11.6

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


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

$\Rightarrow 453.6=210+21x$

$\Rightarrow 453.6-210=243.6=21x$
$\Rightarrow x=11.6cm$
$\therefore$ The perpendicular distance from other vertex is 11.6 cm.