Is there a formula to find out the perimeter of an irregular shape on lattice points when you already know the area?
I am asking this as I have a test tomorrow, and one of the questions that could come up is the area/perimeter of an irregular shape on lattice points. I already know how to find out the area using Pick's theorem, however there doesn't seem to be anything on the internet which talks about finding out the area by a formula and when you already know the area. This website could help though. So, is there a formula to find out the perimeter of an irregular shape on lattice points when you already know the area?
Also, is there a way to find out the perimeter of an irregular shape when you already know the area, but the shape isn't on lattice points? Thanks!
Best Answer
Use the distance formula repeatedly for each side.
Distance Formula
Distance between two points whose coordinates are $(x_1 , y_1)$ and $(y_1 , y_2)$ is given by the formula $$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} $$
This can be proved using the Pythagoras theorem.
For simplicity, you can set the origin at one end of the sides to simplify the formula each time.