Find the area of a parallelogram if its sides are 16 cm, 21 cm, the angle between them is 135 degrees.

1. Vertices of the parallelogram – A, B, C, D. 4. – area of the parallelogram. BC = 21 cm. AB = 16

see Height BE (drawn to the AD side). ∠ABС = 135 °.

2. ∠ABE = ∠ABS – ∠CBE = 135 ° – 90 ° = 45 °.

3. We calculate the length of the height BE through the cosine ∠ABE, equal to the quotient of dividing the height BE,

which is a leg in a right-angled triangle ABE, to the hypotenuse AB:

BE: AB = tangent ∠ABE = tangent 45 ° = √2 / 2.

BE = AB x √2 / 2 = 16 x √2 / 2 = 8√2 cm.

4. S = BC x BE = 21 x 8√2 = 168√2 cm².

Answer: S is equal to 168√2 cm².