SOLUTION: {{{A=1/2}}}{{{abs(matrix(3,3,a,b,1,c,d,1,e,f,1))}}}

Algebra ->  Algebra  -> Surface-area -> SOLUTION: {{{A=1/2}}}{{{abs(matrix(3,3,a,b,1,c,d,1,e,f,1))}}}      Log On

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Question 148413: A=1%2F2abs%28matrix%283%2C3%2Ca%2Cb%2C1%2Cc%2Cd%2C1%2Ce%2Cf%2C1%29%29
Answer by Edwin McCravy(6936) About Me  (Show Source):
You can put this solution on YOUR website!

A=1%2F2abs%28matrix%283%2C3%2Ca%2Cb%2C1%2Cc%2Cd%2C1%2Ce%2Cf%2C1%29%29

That's the formula for the area of a triangle whose
vertices are (a,b), (c,d), and (e,f) going around the
triangle counter-clockwise.

Example:

Suppose we want to find the area of the triangle whose
vertices are (4,3), (-5,7), (3,-6).   Those are in
counter-clockwise order.

drawing%28400%2C400%2C-8%2C8%2C-8%2C8%2C+grid%281%29%2C%0D%0Atriangle%284%2C3%2C-5%2C7%2C3%2C-6%29+++%29

We just plug those corner points into the formula:

A=1%2F2abs%28matrix%283%2C3%2C4%2C3%2C1%2C-5%2C7%2C1%2C3%2C-6%2C1%29%29=%281%2F2%2985=+42.5

Edwin