Question 520826: A hexagon has the following vertices: A (3, 0), B (7, 0), C (9, 2), D (7, 4), E (3, 4), F (1, 2) find the area
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A hexagon has the following vertices: A (3, 0), B (7, 0), C (9, 2), D (7, 4), E (3, 4), F (1, 2) find the area
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A B C D E F A
3 7 9 7 3 1 3
0 0 2 4 4 2 0
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Add the diagonal products starting at the upper left
3*0 + 7*2 + 9*4 + 7*4 + 3*2 + 1*0 = 0 + 14 + 36 + 28 + 6 + 0 = 84
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Add the diagonal products starting at the lower left
0*7 + 0*9 + 2*7 + 4*3 + 4*1 + 2*3 = 0 + 0 + 14 + 12 + 4 + 6 = 36
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The area is 1/2 the difference = (84 - 36)/2
Area = 24 sq units
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This method works for ANY polygon
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