The answer to my question is far beyond my knowledge (as I believe a basic knowledge of calculus is needed) -- so I'm hoping that I might be able to get someone to give me the answer here... My need for an answer has a practical reason -- I'm trying to calculate the ground-fill needed to level an rectangular, area that is currently sloped. (The gravel/fill company is unable to calculate the volume-value for me.)
This is the basic dimensions and description of the "object".
Starting with the top of the object (which is the resulting level plane of land), the dimensions are 20ft x 36ft (rectangular). The four corners have four varying heights to the existing ground level: h1=2ft, h2=.67ft (2/3), h3=0ft, and h4=1ft (the h-values are given in a clockwise sequence). The h sides are all considered to be perpendicular (90deg) to the top plane (the top of object) I'm hoping that this is enough information to calculate the volume (in cubic feet) between the top plane and the (estimated flat) bottom plane.
I've spent hours online looking for a calculator the would give me the result -- and was surprised that I couldn't find such a practical item. So, the result of this problem would be very much appreciated.
Edit1: the dimensions are actually 20x32 (not 20x36)
EDIT2: the distance between h1 and h2 is 20ft, and consequently the distance btw h2 and h3 is 32ft (not 36ft)