Find the perimeter of parallelogram ABCD, if BC is 8, the height drawn from point B is 3, angle D is 150.

1. The ВK height is drawn to the AD side.

2. ∠А = 180 ° – ∠D = 180 – 150 ° = 30 °.

3. We calculate the length AB through the sine ∠A, equal to the quotient of dividing the height of the ВK (leg

right-angled triangle ABK) on AB (hypotenuse of the specified triangle):

ВK: AB = sine ∠A = sine 30 ° = 1/2.

AB = ВK: 1/2 = 3: 1/2 = 6 centimeters.

4.Considering that the sides of a parallelogram opposite each other are equal, its

perimeter (P) is calculated by the formula:

P = 2 (AB + BC) = 2 (6 + 8) = 28 centimeters.