Area Subdivision Methods
For a trapezoid with parallel sides a and b and depth d, the total area is (a+b)/2 * d. When cutting parallel to sides a and b, the cutting line at distance x from side a has width: w(x) = a + (b-a)*x/d. The area from side a to x is: A(x) = a*x + (b-a)*x^2/(2d). This quadratic equation is solved for each cutting position.