<PRE><B>Question 393219</B>
The vertices of triangle ABC have (x,y) coordinates (4,5), (5,3) and (1,3) respectivly.  What is the area of triangle ABC?
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There&#39;s more than one way to do this, and problems like it.
Here&#39;s one:
Write the points in columns repeating the 1st point
A B C A
4 5 1 5
5 3 1 4
Add the diagonal products from upper left, then from lower left
Upper:
4*3 + 5*1 + 1*4 = 12 + 5 + 4 = 19
Lower:
5*5 + 3*1 + 1*5 = 25 + 3 + 5 = 33
Find the difference, 33 - 19 = 14
The area is 1/2 that, = 7 sq units.
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This method works for all polygons, any # of sides.

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