SOLUTION: The vertices of triangle ABC have (x,y) coordinates (4,5), (5,3) and (1,3) respectivly. What is the area of triangle ABC? if you can show me how to solve this problem please em

Question 393219: The vertices of triangle ABC have (x,y) coordinates (4,5), (5,3) and (1,3) respectivly. What is the area of triangle ABC?
if you can show me how to solve this problem please email me at mkhla@aol.com. Thanks!!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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's more than one way to do this, and problems like it.
Here'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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