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isosceles trapezoid and areas, computational (Greece Junior 2004)

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July 12, 2019
geometrytrapezoidisoscelesareas

Problem Statement

Let ABCDABCD be a rectangle. Let K,LK,L be the midpoints of BC,ADBC, AD respectively. From point BB the perpendicular line on AKAK, intersects AKAK at point EE and CLCL at point ZZ. a) Prove that the quadrilateral AKZLAKZL is an isosceles trapezoid b) Prove that 2SABKZ=SABCD2S_{ABKZ}=S_{ABCD} c) If quadrilateral ABCDABCD is a square of side aa, calculate the area of the isosceles trapezoid AKZLAKZL in terms of side BC=aBC=a
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