Question 1154678
How do you find the area of a polygon ABCDE with vertices A(0,0), B(0,4), C(8,8), D(14,0), and E(9,-2)
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There's more than one way.
The simplest, IMO, is this:
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<pre>

 A    B    C    D    E    A
 0    0    8   14    9    0
 0    4    8    0   -2    0
</pre>

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Add the diagonal products starting at the upper left.
0*4 + 0*8 + 8*0 + 14*-2 + 9*0 = 0+0+0-28+0 = -28
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Add the diagonal products starting at the lower left.
0*0 + 4*8 +8*14 + 0*9 + -2*0 = 0+32+112+0+0 = 144
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The difference is 172
The area is 1/2 that = 86 sq units.
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The points have to be in order around the figure.
I think it works for all polygons, not just convex.
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PS  Graphing it is a good idea, to ascertain that the points are in order around the polygon.