How to use Monte Carlo simulation to calculate the area of polygon?

Hi, I want to use Monte Carlo simulation to calculate the area of polygon.

The polygon area is defined with longitude and latitude. (in degrees)

I've found the bounding box of the polygon, but I have no idea how to apply Monte Carlo to randomly create dots and caculate the area.

Can anyone help calculating the area of this polygon using Monte Carlo simulation?

Answer 1

[Torsten]

Randomly create points inside the bounding box.

Decide which of the points are inside (P_i) and which of the points are outside (P_a) the polygon.

If the area of the bounding box is A, an approximation for the area A_p of the polygon is

A_p = A*#P_i/(#P_i + #P_a)