# In parallelogram ABCD, BD is perpendicular to AB, BE is perpendicular to AD, BE = 6cm, AE = 3cm.

September 14, 2021 | education

| **In parallelogram ABCD, BD is perpendicular to AB, BE is perpendicular to AD, BE = 6cm, AE = 3cm. Find the area of the parallelogram.**

By condition DB is perpendicular to the lateral side AB, then triangle ABD is rectangular, and its height BE is drawn to the hypotenuse from a right angle.

Then BE = √ (AE * DE).

We square both sides of the equality and express DE.

BE ^ 2 = AE * DE.

DE = BE ^ 2 / AE = 36/3 = 12 cm.

Then the length of the base is AD = AE + DE = 3 + 12 = 15 cm.

Determine the area of the parallelogram.

Savsd = AD * BE = 15 * 6 = 90 cm2.

Answer: The area of the parallelogram is 90 cm2.

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