In an isosceles trapezoid, the angle at the base is 60 °, and the bases are 6 and 10 cm. What is the perimeter of the trapezoid?
Since the trapezoid is isosceles, then AB = CD.
We omit the height of the trapezoid from the vertex B, in the formed right-angled triangle the leg AH will be equal to:
AH = (AD – BC) / 2 = (10 – 6) / 2 = 2 cm.
The angle ABH of the triangle is 180 – 90 – 60 = 30, then the length of the hypotenuse AB is equal to two lengths of the leg AH, since the leg lies opposite the angle of 30 degrees. AB = 2 * AH = 2 * 2 = 4 cm.
Then the perimeter of the trapezoid is: P = 2 * AB + BC + AD = 8 + 6 + 10 = 24 cm.
Answer: P = 24 cm
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