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MMO 249 Moscow MO 1953 quadrilateral area S <= (a + c)(b + d)/4}

Source:

August 9, 2019

geometryareasgeometric inequality

Problem Statement

Let

a, b, c, d

be the lengths of consecutive sides of a quadrilateral, and

S

its area. Prove that

S \le \frac{ (a + b)(c + d)}{4}