Question

How do you find the area of a triangle plot as point A = (-2,5); B = (12,3); C = (10,-11)?

Answer 1

I found `100` units of area

Explanation:

There may be different ways to solve this but I thought of one that is quite intriguing:
Area=`+-1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|`
i.e. `1/2` times the determinant formed using your coordinates and a column of `1` (the `+-` is to "correct" possible negative values).
So, in your case:
Area=`+-1/2|(-2,5,1),(12,3,1),(10,-11,1)|=+-1/2(-200)=100` u.a.
"correcting" the minus sign.

The demonstration and reference of the above method can be found in: