The sides of the parallelogram are 4cm and 5cm, the angle between them is 45 degrees. Find the heights of the parallelogram.

univerkov | February 8, 2021 | education

Let us determine the area of the parallelogram through the lengths of its sides and the angle between them.

Savsd = AВ * AD * SinВAD = 4 * 5 * Sin45 = 20 * √2 / 2 = 10 * √2 cm2.

Also the area of the parallelogram is equal to: Savsd = AD * ВН.

ВН = Savsd / AD= 10 * √2 / 5 = 2 * √2 cm.

Savsd = СD * ВK.

ВK = Savsd / СD = 10 * √2 / 4 = 2.5 * √2 cm.

Answer: The heights of the parallelogram are 2 * √2 cm and 2.5 * √2 cm.

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