Question 384731: If A(1,2), B(5,6) and C(-2,-5) are the vertices of a triangle ABC, find the area of triangle ABC.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If A(1,2), B(5,6) and C(-2,-5) are the vertices of a triangle ABC, find the area of triangle ABC.
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There's a little known method that works for all polygons, regardless of the number of sides.
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List the points in columns, repeat the 1st point
A B C A
1 5 -2 1
2 6 -5 1
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Starting at the left, add the diagonal products "upward" and "downward"
Upward: 2*5 + 6*-2 + -5*1 = 10 - 12 - 5 = -7
Downward: 1*6 + 5*-5 + -2*1 = 6 - 25 - 2 = -21
The difference = 14
The area is 1/2 that, = 7 sq units
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