Calculate the area of an isosceles trapezoid in which the diagonal forms an angle of 60

| May 25, 2021 | education

Calculate the area of an isosceles trapezoid in which the diagonal forms an angle of 60 degrees with a large base. BD = 24, AK = 6, angle BDK = 60 degrees.

In a right-angled triangle ВDК, through the hypotenuse and the angle, we determine the length of the legs ВK and DК.

Cos60 = DK / BD, then DK = BD * Cos60 = 24 * 1/2 = 12 cm.

Sin60 = ВK / ВD, then ВK = ВD * Sin60 = 24 * √3 / 2 = 12 * √3 cm.

Determine the length of the larger base. AD = AK + DK = 6 + 12 = 18 cm.

Since the trapezoid is isosceles, then DH = AK = 6 cm, then KH = AD – 2 * AK = 18 – 12 = 6 cm.

ВСНK is a rectangle, then BC = НK = 6 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВK / 2 = (6 + 18) * 12 * √3 / 2 = 144 * √3 cm2.

Answer: The area of the trapezoid is 144 * √3 cm2.



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