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Correct option is D)

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 =

$∣∣∣∣∣ 2(x_{1}y_{2}−y_{1}x_{2})+(x_{2}y_{3}−y_{2}x_{3})...+(x_{n}y_{1}−y_{n}x_{1}) ∣∣∣∣∣ $

where $a_{1}$ is the coordinate of vertex 1 and $y_{n}$ is the y-coordinate of the nth vertex etc.

Area $∣∣∣∣∣ 2[(−3×2)−(2×1)]+[(1×−3)−(3×2)]+[(3×−6)−(−3×0)]+[(−4×−2)−(−2×−3)]+[(0×−2)−(−6×−4)] ∣∣∣∣∣ =∣∣∣∣∣ −273 ∣∣∣∣∣ =273 $

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

Area$=21 bh= ×−6=224 =12$ square unit

Angle subtended by BD at $A=tan_{−1}(6182 )$

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