One side of the parallelogram is 12, the other is 5, and one of the angles is 45 °. Find the area of the parallelogram.

univerkov | November 22, 2020 | education

Let’s draw the height BH
Triangle ABH:
Rectangular and isosceles, since angle = 45
then AH = AB = 5
By the Pythagorean theorem:
BH ^ 2 = AH ^ 2 + AB ^ 2
BH ^ 2 = 50
BH = 5√2
S = BH * AD
S = 5√2 * 12 = 60√2

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