Question

The area of the triangle formed by points $(0,0)\left(3,\frac{\pi }{2}\right)and(3,\frac{\pi }{6})$ is

Answer 1

Area of a triangle$=\Delta =\frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|$

$=\frac{1}{2}\left|\begin{array}{ccc}0& 0& 1\\ 3& \frac{\pi }{2}& 1\\ 3& \frac{\pi }{6}& 1\end{array}\right|$

$=\frac{1}{2}[0-0+1(\frac{3\pi }{6}-\frac{3\pi }{2})]$

$=\frac{1}{2}(\frac{3\pi }{6}-\frac{9\pi }{6})$

$=\frac{1}{2}\times -\frac{6\pi }{6}$

$=\frac{-\pi }{2}$

But area is always positive.

Hence area of the triangle$=\frac{\pi }{2}$ sq.units