Calculate the area of the parallelogram if its sides are 6cm and 11cm, and the height forms

Calculate the area of the parallelogram if its sides are 6cm and 11cm, and the height forms an angle of 30 ° on the smaller side.

1. Vertices of the parallelogram – A, B, C, D. S – area of the parallelogram. ВK – height (drawn to the AD side). ∠АВК = 30 °. AB = 6 centimeters. AD = 11 centimeters.

2. We calculate the length of the height ВK through the cosine ∠АВК:

BK: AB = cosine ∠ABK = cosine 30 ° = √3 / 2.

BK = AB x √3 / 2 = 6 x √3 / 2 = 3√3 centimeters.

3. S = AD x BK = 11 x 3√3 = 33√3 centimeters².

Answer: S equals 33√3 centimeters².