Can you solve the volume of "a cube" with unequal heights? I have a challenge for someone (which I plan on working on this weekend myself when I have free time from my homework). Can you calculate the volume of a cube-like shape with four different heights and with perfect square base if you are given the surface area of all sides, including the base, except for its top? The sides of this object would be four trapezoids of which two, and only two, heights each side would be equal (where the two trapezoids meet to create a corner). The angle of the trapezoid to its neighbor and the square base is always 90 degrees. To get a better idea of what I am taking about, check out the picture I uploaded to this post. I would be very grateful to whomever can solve this for me. Knowing a formula for this would be very useful for a school project I am creating. In case you were wondering why I want to know this (for motivational purposes), I am trying to map the the volume of space shaded by irregular objects with a light source coming from a given angle (so I can ask an interesting sunlight competition question for my undergraduate senior project in plant ecology). From what I can tell at this point, field measurements could yield an average volume that would be represented by a shape similar to the one I've described (because I believe I've already figured out a way to find the area of all the sides and the base). I was just hoping a solution already existed for this (so I don't have to reinvent the wheel). Thanks for taking the time to check out my question.