Question 1033634: Find the area of the polygon defined by the coordinates (0, -5), (-5, 0), (-15, -20), and (-20, -15).
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the area of the polygon defined by the coordinates (0, -5), (-5, 0), (-15, -20), and (-20, -15).
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Put the points in order around the quadrilateral:
A(0,-5), B(-5,0), C(-20,-15), and D(-15,-20).
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Make a matrix, repeating the 1st point:
A...B...C.....D..A
0 -5 -20 -15 0
-5 0 -15 -20 -5
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Add the diagonal products starting at the upper left
0*0 + -5*-15 + -20*-20 + -15*-5 = 0 + 75 + 400 + 75 = 550
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Add the diagonal products starting at the lower left
-5*-5 + 0*-20 + -15*-15 + -20*0 = 25 + 225 = 250
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The area is 1/2 the absolute value of the difference.
Area = (550 - 250)/2
Area = 150 sq units
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PS This method works for any polygon, regular or not, but the points have to be in order.
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