Given an isosceles trapezoid ABCD. The lines at the base are 6 cm and 12 cm. The angle at the base is 60 degrees.

| January 7, 2021 | education

Given an isosceles trapezoid ABCD. The lines at the base are 6 cm and 12 cm. The angle at the base is 60 degrees. Find the perimeter and sides of the trapezoid.

Let us draw the height ВН from the top B of the trapezoid. In an isosceles trapezoid, the height lowered from the apex of an obtuse angle divides the larger base into two segments, the smaller of which is equal to the half-difference of the bases, and the larger one, half the sum.
Then АН = (AD – ВС) / 2 = (12 – 6) / 2 = 3 cm.
In a right-angled triangle ABН, by condition, the angle ABН = 60, then the angle ABН = 180 – 90 – 60 = 30. The leg AH lies opposite the angle 300, and accordingly is equal to half the length of the hypotenuse CB, then AB = 2 * AH = 2 * 3 = 6 cm.
Since the trapezoid is isosceles, then СD = AB = 6 cm.
Let’s define the perimeter of the trapezoid.
R = AB + BC + СD + AD = 6 + 6 + 6 + 12 = 30 cm.
Answer: The sides are 6 cm, the perimeter is 30 cm.
Answer: The middle line of the trapezoid is 7 cm.



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