# Diagonal BD of parallelogram ABCD is perpendicular to side AD

January 25, 2021 | education

| **Diagonal BD of parallelogram ABCD is perpendicular to side AD Find the area of parallelogram ABCD if AB = 8 cm and angle A = 30 degrees.**

Since the diagonal of the BD is perpendicular to the side of the BP, the ABD triangle is rectangular.

In a right-angled triangle of the ABD, the leg of the BD lies opposite the angle of 300, then its length is equal to half the length of the hypotenuse AB.

BD = AB / 2 = 8/2 = 4 cm.

By the Pythagorean theorem, we determine the length of the leg of AD.

AD ^ 2 = AB ^ 2 – BD ^ 2 = 64 – 16 = 48.

AD = 4 * √3 cm.

Determine the area of the parallelogram.

Savsd = AD * BD = 4 * √3 * 4 = 16 * √3 cm2.

Answer: The area of the parallelogram is 16 * √3 cm2.

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