Question 687872: Find the area of quadrilateral formed with vertices (3,-5),(5,-1),(2,1),(-3,-2)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the area of quadrilateral formed with vertices (3,-5),(5,-1),(2,1),(-3,-2)
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Label the points:
A(3,-5), B(5,-1), C(2,1), D(-3,-2)
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.A...B...C...D...A
+3 +5 +2 -3 +3 x values
-5 -1 +1 -2 -5 y values
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Add the diagonal products starting upper left
3*-1 + 5*1 + 2*-2 + -5*-5 = -3 + 5 - 4 + 25 = 13
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Add the diagonal products starting lower left
-5*5 + -1*2 + 1*-3 + -2*3 = -25 - 2 - 3 - 6 = -36
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Area = 1/2 the difference = 49/2 sq units
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This method works for ALL polygons, any # of sides.
The points have to be entered in order around the polygon, tho.
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