MathDB

The polyhedron

PABCDQ

has the form shown in the figure. It is known that

ABCD

is parallelogram, the planes of the triangles of the

PAC

and

PBD

mutually perpendicular, and also mutually perpendicular are the planes of triangles

QAC

and

QBC

. Each face of this polyhedron is painted black or white so that the faces that have a common edge are painted in different colors. Prove that the sum of the squares of the areas of the black faces is equal to the sum of the squares of the areas of the white faces. https://1.bp.blogspot.com/-UM5PKEGGWqc/X1V2cXAFmwI/AAAAAAAAMdw/V-Qr94tZmqkj3_q-5mkSICGF1tMu-b_VwCLcBGAsYHQ/s0/2007.5%2Bchampions%2Btourn.png

Problem Statement