The coordinates of each vertex of the quadrilateral ABCD are a (0.0), B (3.5), C (12.8) and D (15.0). Find the area of the quadrilateral

You can easily calculate the area by making a graph
Let BM be perpendicular to AD and m, cn be perpendicular to AD and n
Area = triangle ABM area + trapezoid bmnc area + triangle CND area
= 1/2×3×5 + (5+8)×(12-3)/2 + 1/2×(15-12)×8
= 15/2 + 117/2 + 12
= 78

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