# Find the side of an isosceles trapezoid whose base is 12 and 6 cm and one of the angles is 120 degrees.

August 29, 2021 | education

| The solution of the problem:

An isosceles trapezoid ABCD is given. From the corner B and C to a larger base, we will draw the height of BK and CM. Consider a triangle ABK. The ABK angle is 120 – 90 = 30 degrees. The side of the AK is (12 – 6) / 2 = 3 centimeters. The ABK triangle is rectangular. In a right-angled triangle, the leg lying opposite an angle of 30 degrees is half the hypotenuse. The hypotenuse AB of the ABK triangle is the lateral side of the isosceles trapezium ABCD.

1. Find the side of the trapezoid.

AB = 2 * AK = 2 * 3 = 6 cm.

Answer: The side is 6 cm.

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