Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the case of polygon triangle picking,
(1)
 
(2)

The distribution of areas, illustrated above, is apparently not known exactly.
Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the case of polygon triangle picking,
(1)
 
(2)

The distribution of areas, illustrated above, is apparently not known exactly.
Weisstein, Eric W. "Pentagon Triangle Picking." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/PentagonTrianglePicking.html