The length of the side of an isosceles trapezoid is 16cm, and the degree measure

The length of the side of an isosceles trapezoid is 16cm, and the degree measure of one of its angles is 150 degrees. Calculate the perimeter of the trapezoid if its area is 88cm2.

1. Vertices of the trapezoid – A, B, C, D. S – area. B = 150 °. ВН – height. P is the perimeter.

2. ∠АВН = ∠В – ∠СВН = 150 ° – 90 ° = 60 °.

3. We calculate the height of the ВН using one of the trigonometric functions ∠АВН (cosine):

ВН: AB = cosine ∠ABН = cosine 60 ° = 1/2.

BH = AB x 1/2 = 16 x 1/2 = 8 cm.

4. Calculate the total length of the sides BC and AD, using the formula for calculating S:

S = (ВС + АD) / 2 х ВН = 88 cm².

BC + AD = 88 x 2: 8 = 22 cm.

5.P = CD + AB = BC + AD = 16 + 16 + 22 = 54 cm.

Answer: P is 54 cm.