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. 15.4
• C. 19.2
• D. 21.1

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 x
Therefore, area of quadrilateral = Area of $\Delta$ ADC + Area of $\Delta$ ABC
$\Rightarrow$ $453.6$ = $\frac{1}{2}$ $\times$ 42 $\times$ 10 + $\frac{1}{2}$ $\times$ 42 $\times$ x

[Area of triangle = 0.5 x product of height and base.]

$\Rightarrow$ 453.6 $=210+21\times x$

$\Rightarrow$ 453.6 - 210 $=21\times x$

$\Rightarrow$ 243.6 $=21\times x$

$\Rightarrow$ $\frac{243.6}{21}=x$
$\Rightarrow$ x = 11.6 cm