Question 631915: Find the area of trapezoid ABCD if the vertices are A(1,5), B(7,3),C(2,-4), and D(-7,-1)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the area of trapezoid ABCD if the vertices are A(1,5), B(7,3),C(2,-4), and D(-7,-1)
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Do these like this:
+A +B +C +D +A
+1 +7 +2 -7 +1
+5 +3 -4 -1 +5
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Add the diagonals starting at the upper left.
= 1*3 + 7*-4 + 2*-1 + -7*5 = 3 - 28 - 2 - 35 = -62
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Add the diagonals starting at the lower left.
= 5*7 + 3*2 + -4*-7 + -1*1 = 35 + 6 + 28 - 1 = +68
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Then,
Area = 1/2 the absolute value of the difference
Diff = 130
Area = 65 sq units.
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This works for all polygons, any number of sides.
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