Question

Area of parallelogram in coordinate geometry

Answer 1

Find the area of the parallelogram that has coordinates of A(-2,2), B(-4,-2), C(2,-2), and D(4,2). 
Answer by Alan3354(59252)   (Show Source): You can put this solution on YOUR website!
Find the area of the parallelogram that has coordinates of A(-2,2), B(-4,-2), C(2,-2), and D(4,2)
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Arrange the points as a 2 by 5 matrix:
A.. B.. C.. D.. A
-2 -4 +2 +4 -2
+2 -2 -2 +2 +2
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Add the diagonal products starting at the upper left:
-2*-2 + -4*-2 + 2*2 + 4*2 = 4+8+4+8 = 24
Add the diagonal products starting at the lower left:
2*-4 + -2*2 + -2*4 + 2*-2 = -8-4-8-4 = -24
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The area = 1/2 the difference = 1/2*48
Area = 24 sq units
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There are other way to do a parallelogram that might be easier, but this method works for ALL polygons with any number of sides.