Finding area of Figures

[nsguy1350]

I see some questions on finding areas of quadrilaterals sometimes. These are irregular quadrilaterals, not parallelograms or anything. How can I find the area? They give a coordinate grid of some sort, and then you have to find the area of the figure. I cannot find an example right now, but hopefully you know what I'm talking about (I think there was one on this year's TMSCA State test, not 100% sure though.)

[007math]

Count the squares. :D
Never failed for my friend.

[nsguy1350]

Once you start getting fractional squares though, and the answers are 1/2 unit apart... what do you do?

[Salvadoramerican]

Split it into triangles and use matrices to find the area of each
An example would be district 1 2007 #29
(-4,3)(-3,-2)(1,2)(4,-3)
split it into two triangles (-4,3)(-3,-2)(1,2) and (-3,-2)(1,2)(4,-3)

Set up the matrices
[unparseable or potentially dangerous latex formula] [unparseable or potentially dangerous latex formula]

make the determinant positives though

[007math]

[Capybara]

You can find a rectangle that circumscribes the figure, and take out the areas you don't want. Usually much faster.

[nsguy1350]

[strr]

use pick's theorem. seems like it's a whole lot faster than matrices in my opinion.

[nsguy1350]

[strr]

We learned it in geometry, but my coach reminded me about it this year.

[sxk1693]

whoah!! who invents these theorems