How do you use the rectange method to approximate area for ambigous shapes?

This isn't exactly the kind of thing we are taught in Calculus to measure. You would just need to print that image along with its proper scale. Just draw rectangles that are small in width (the smaller, the more approximate). Make the rectangles have an intersection with the borders of land at the midpoint of it's width. Do this for all rectangles. Find the area, and add them all up.