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Suppose that

`R`

is the region bounded by

`y=e^(x)`

, the

`x`

-axis, the

`y`

-axis and

`x=2`

. Find the volume of the solid whose base is

`R`

and has cross-sections perpendicular to the

`x`

-axis which are triforces. A triforce is an equilateral triangle with an equilateral triangle removed from the center. Equivalently, it is three equilateral triangles where one is stacked on top of the other two. An example of a triforce is provided below, where the corresponding area is colored black.