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Square divided into two triangles and a parellelogram of equal areas

Source: Cyprus 2022 Junior TST-1 Problem 2

February 21, 2022
geometrysquareareaparallelogram

Problem Statement

Let ABCDABCD be a square. Let E,ZE, Z be points on the sides AB,CDAB, CD of the square respectively, such that DE∥BZDE\parallel BZ. Assume that the triangles △EAD,△ZCB\triangle EAD, \triangle ZCB and the parallelogram BEDZBEDZ have the same area.
If the distance between the parallel lines DEDE and BZBZ is equal to 11, determine the area of the square.
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