The sides of the parallelogram are 5 and 8, and the cosine of one of the angles is -V2 / 2. find the area of the parallelogram.

1. Vertices of the parallelogram – A, B, C, D. AB = 5 units. AD = 8 units.
BH – height. S is the area of the parallelogram. Cosine ∠A = √2 / 2.
2. Cosine ∠A = √2 / 2. ∠А = 45 °.
3. We calculate the length of the height of the BH through one of the trigonometric functions ∠А (sine):
BH / AB = sine ∠A = sine 45 ° = √2 / 2.
BH = 5 x √2 / 2 = 2.5√2 units of measurement.
4. S = AD x BH = 8 x 2.5√2 = 20√2 units of measurement².
Answer: S equals 20√2 units of measurement².