Question 698409: Three straight paths in a park form a triangle with vertices at: A(-24,16) B(56,-16) and C(-72,-32).
determine the area of triangle ABC
hint: you will have to find the length of an altitude and the area of any triangle is half base of the triangle times it's height
i have no clue on how to do this
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Three straight paths in a park form a triangle with vertices at: A(-24,16) B(56,-16) and C(-72,-32).
determine the area of triangle ABC
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Do it like this.
.A......B.....C.....A
-24 +56 -72 -24
+16 -16 -32 +16
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Add the diagonal products starting upper left.
-24*-`16 + 56*-32 + -72*16 = 384 - 1792 - 1152 = -2560
Add the diagonal products starting lower left.
16*56 + -16*-72 + -32*-16 = 896 + 1152 + 512 = 2560
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The area = 1/2 the difference = 2560 sq units
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It's a different method, not well known.
It works for polygons with any number of sides.
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