Two sides of a parallelogram = 6 cm and 8√2 cm, and the angle between them is 135 °. Find the area of a parallelogram.

Parallelogram AВСD:
AB = СD = 6 cm
BC = AD = 8√2 cm
Angle ABC = СDA = 135 degrees.
Let’s draw the height of the HВ
Consider the triangle ABН:
angle AНВ = 90 degrees.
angle AВН = 45 degrees. (135-90)
By the theorem on the sum of angles in a triangle, we find out that AVN = VAN = 45 degrees, so the side AH = BH
Let side AH and BH = x
By the Pythagorean theorem:
x ^ 2 + x ^ 2 = 6 ^ 2
2x ^ 2 = 36
x ^ 2 = 18
x = 3√2 cm
3√2 cm = AH = BH
S parallelogram = ah = 8√2 * 3√2 = 48 cm square
Answer: 48 cm square.