In an isosceles trapezoid ABCD, the segment BF is parallel to the side of the CD, the angles adjacent

| April 25, 2021 | education

In an isosceles trapezoid ABCD, the segment BF is parallel to the side of the CD, the angles adjacent to the side of AD are 60 degrees. The perimeter of four angles FBCD is 28 cm. Find the perimeter of the trapezoid if its side is 6 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 = 6 cm.

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

Then P = 28 = BC + FD + CD + BF.

(ВС + FD) = 28 – 6 – 6 = 16 cm.

BC = FD = 16/2 = 8 cm.Then AD = AF + FD = 6 + 8 = 14 cm.

Determine the perimeter of the trapezoid. P = 6 + 8 + 6 + 14 = 34 cm.

Answer: The perimeter of the trapezoid is 34 cm.



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