MathDB

Right triangular prism

ABCDEF

with triangular faces

\vartriangle ABC

and

\vartriangle DEF

and edges

\overline{AD}

\overline{BE}

, and

\overline{CF}

has

\angle ABC = 90^o

and

\angle EAB = \angle CAB = 60^o

. Given that

AE = 2

, the volume of

ABCDEF

can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Compute

m + n

. https://cdn.artofproblemsolving.com/attachments/4/7/25fbe2ce2df50270b48cc503a8af4e0c013025.png

Problem Statement