SOLUTION: Given A (-3, 2), B (2, 7) and C (8, 10), find the area of the triangle ABC.

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Question 1101896: Given A (-3, 2), B (2, 7) and C (8, 10), find the area of the triangle ABC.
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!

Alan,
What is this process called? What is the rational behind it?
x -3,2,8,-3
y 2,7,10,2
add
-3*7+2*10+8*2
-21+20+16=15
add
2*2+7*8+(10*-3)=30
4+56-30=30
subtract
15-30=-15
1/2*|-15|=7.5 sq units
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Given A (-3,2), B (2,7) and C (8,10), find the area of the triangle ABC.
=========
 A   B   C   A
-3   2   8  -3
 2   7  10   2
------

---
Add the diagaonal products starting upper left.
-3*7 + 2*10 + 8*2 = 15
Add the diagaonal products starting lower left.
2*2 + 7*8 -3*10 = 30
---------
The difference is 15.
The area is 1/2 that = 7.5 sq units
==================
Works for all polygons, any # of sides.
The points have to be in order around the polygon.
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