Question
All parallelograms having equal areas have same perimeters. Observe all the four triangles $FAB, EAB, DAB$ and $CAB$ as shown in Fig. :
All triangles have the same base and the same altitude.

Answer

It is clear from the figure that all triangles have same base $AB$ and all the vertices lie on the same line, so the distance between vertex and base of triangle (i.e. length of altitude) are equal.

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