# In isosceles trapezoid ABCD, segment BF is parallel to side CD, and the angles adjacent to side AD

In isosceles trapezoid ABCD, segment BF is parallel to side CD, and the angles adjacent to side AD are 60. The perimeter of quadrilateral FBCD is 20 cm. Find the perimeter of trapezoid ABCD if its side face is 4 cm.

Let’s prove it. That triangle ABF is equilateral.

The angle BAD = CDA, according to the condition, is equal to 60, then the angle BFA = 60, as corresponding to the angle CDA when crossing the parallel straight lines CD and BF of the secant AD.

In triangle ABF, two angles are equal to 60, then the triangle is equilateral. Then AB = BF = AF = 4 cm.

The quadrilateral BCDF is a parallelogram, since its opposite sides are parallel.

Then P = 20 = BC + FD + CD + BF.

(BC + FD) = 20 – 4 – 4 = 12 cm.

BC = FD = 12/2 = 6 cm.Then AD = AF + FD = 4 + 6 = 10 cm.

Determine the perimeter of the trapezoid. P = 4 + 6 + 4 + 10 = 24 cm.

Answer: The perimeter of the trapezoid is 24 cm.

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