BG-MO 1977 Problem 3

A given truncated pyramid has triangular bases. The areas of the bases are $B_1$ and $B_2$ and the area of the surface is $S$ . Prove that if there exists a plane parallel to the bases whose intersection divides the pyramid to two truncated pyramids in which may be inscribed by spheres then $$S=(\sqrt{B_1}+\sqrt{B_2})(\sqrt[4]{B_1}+\sqrt[4]{B_2})^2$$ G. Gantchev