Find the area of a parallelogram, if one side is 5, the other side is 4√2, the angle A is 45 degrees.

univerkov | July 6, 2021 | education

Find the area of a parallelogram, if one side is 5, the other side is 4√2, the angle A is 45 degrees. A parallelogram ABCD is given.

Let’s build the height BH. Triangle ABH is rectangular and isosceles, since the angle is A = 45, then BH = AH.

By the Pythagorean theorem, AB ^ 2 = AH ^ 2 + BH ^ 2 = 2 * BH ^ 2.

BH ^ 2 = AH ^ 2/2 = 32/2 = 16.

BH = 4 cm.

Then Savsd = AD * BH = 5 * 4 = 20 cm2.

Answer: The area of the parallelogram is 20 cm2.

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