MathDB

In a convex quadrilateral

ABCD

with area

S

, each side was divided into 3 equal parts and segments were drawn connecting the appropriate points of division of the opposite sides in such a way that the quadrilateral was divided into 9 quadrilaterals. Prove that the sum of the areas of the following three quadrilaterals resulting from the division: the one containing the vertex

A

, the middle one and the one containing the vertex

C

is equal to

\frac{S}{3}

Problem Statement