Let $A(0,-6),B(1,2),C(3,-3),D(-3,2),$ and $E(-4,-2)$ be given points, then which of the following is (are) true?

Given the points

A(0,-6), B(1,2), C(3,-3),D(-3,2) and E(-4,-2)

Area of  the pentagon = Area formed by a polygon =

$\left|\frac{(x_1{y}_2-y_1{x}_2)+(x_2{y}_3-y_2{x}_3)...+(x_n{y}_1-y_n{x}_1)}{2}\right|$

where $a_1$ is the coordinate of vertex 1 and $y_n$  is the y-coordinate of the nth vertex etc.

Area $$\begin{gathered} \left|\frac{\left[(-3\times 2)-(2\times 1)\right]+\left[(1\times -3)-(3\times 2)\right]+\left[(3\times -6)-(-3\times 0)\right] \\ +\left[(-4\times -2)-(-2\times -3)\right]+\left[(0\times -2)-(-6\times -4)\right]}{2}\right| \\ =\left|-\frac{73}{2}\right|=\frac{73}{2} \end{gathered}$$

Area of triangle formed by points below $$x-axis,

Area$=\frac{1}{2}bh={}_{}\times -6=\frac{24}{2}=12$ square unit

Angle subtended by BD at $A={\tan }^{-1}\left(\frac{82}{61}\right)$