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**Unenlightened** **Find the volume of the solid lying beneath the surface **$\displaystyle z=xy$ **and above the triangle in the **$\displaystyle x-y$**-plane with vertices **$\displaystyle (1,2),(1,4),(5,2)$.

I can picture this in my head, and while I initially thought to thought to make the shape into a cuboid, and find its area, then half it - the related problems are all integration related, so I figured perhaps I ought to use calculus instead, perhaps some double integral...

Beyond that, though, I'm lost...