The mean triangle area of a triangle picked at random inside a unit cube is A^_ = 0.15107 ± 0.00003, with variance var(A) = 0.008426 ± 4.×10^-6. The distribution of areas, illustrated above, is apparently not known exactly. The probability that a random triangle in a cube is obtuse is approximately Π(3) = 0.5425.

ball triangle picking | cube line picking | cube point picking | square triangle picking