ABCD-isosceles trapezoid: AB = CD = BC, angle A = 60 degrees, large base AD = 10cm. Find the perimeter of the trapezoid.

univerkov | February 10, 2021 | education

By condition, the smaller base of the trapezoid is equal to its lateral sides.

Let AB = BC = СD = 2 * X cm.

We will build the heights of the ВН and СD trapezoid.

In a right-angled triangle ABН CosВAN = AН / AB, then AH = AB * Cos60 = 2 * X / 2 = X cm.

Since the trapezoid is isosceles, then DK = AH = X cm.

In the rectangle ВСKН НK = ВС = 2 * X cm.

Base length AD = AH + НK + DK = X + 2 * X + X = 4 * X cm.

4 * X = 10 cm.

X = 10/4 = 2.5.

Then AB = BC = СD = 2 * 2.5 = 5 cm.

The perimeter of the trapezoid is: Ravsd = 5 + 5 + 5 + 10 = 25 cm.

Answer: The perimeter of the trapezoid is 25 cm.

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