Question

# 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?

A
Area of pentagon formed by these points is 732
B
Area of triangle formed by points below x-axis is 12 square units
C
Angle subtended by BD at A is tan13261
D
All of these
Solution
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#### Given the pointsA(0,-6), B(1,2), C(3,-3),D(-3,2) and E(-4,-2)Area of the pentagon = Area formed by a polygon =∣∣∣(x1y2−y1x2)+(x2y3−y2x3)...+(xny1−ynx1)2∣∣∣where a1 is the coordinate of vertex 1 and yn is the y-coordinate of the nth vertex etc.Area ∣∣ ∣ ∣ ∣∣[(−3×2)−(2×1)]+[(1×−3)−(3×2)]+[(3×−6)−(−3×0)]+[(−4×−2)−(−2×−3)]+[(0×−2)−(−6×−4)]2∣∣ ∣ ∣ ∣∣=∣∣∣−732∣∣∣=732Area of triangle formed by points below \$x-axis,Area=12bh=×−6=242=12 square unitAngle subtended by BD at A=tan−1(8261) 0
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