Question

Sides of a quadrilateral are $9cm,40cm,28cm$ and $15cm$ The angle between the first two sides is a right angle The area of the quadrilateral is

• A. $312c{m}^2$
• B. $280c{m}^2$
• C. $306c{m}^2$
• D. None of these

Answer 1

The correct option is C $306c{m}^2$

Area $\Delta ABC=\frac{1}{2}\times 9\times 40$ cm
$=180c{m}^2$
In $\Delta ABC$
AC = $\sqrt{{40}^2+9^2}cm$
= 41 cm
In $\Delta ADC$
s = $\frac{41+15+28}{2}=42$ cm
Area $\Delta ADC$ = $\sqrt{42(42-41)(42-18)(42-15)}c{m}^2$
$=126c{m}^2$
Area of quadrilateral ABCD $=(180+126)$ $c{m}^2$

$=306c{m}^2$