Question
Find the area of the quadrilateral ABCD, the coordinates
of whose vertices are A(6,-3),B(-4,-2),C(3,1) and D(5,0)?Solution
Vertices: A(6,−3), B(−4,−2), C(3,1), D(5,0) Formula: Area = ½ × |x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁ − (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)| Apply values: = ½ × |6(−2) + (−4)(1) + 3(0) + 5(−3) − [ (−3)(−4) + (−2)(3) + 1(5) + 0(6) ]| = ½ × |−12 −4 + 0 −15 − (12 −6 +5 + 0)| = ½ × |−31 −11| = ½ × 42 = 21
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