In an isosceles trapezoid ABCD with an acute angle of 60, the segment BF is parallel to the CD

| May 3, 2021 | education

In an isosceles trapezoid ABCD with an acute angle of 60, the segment BF is parallel to the CD side and equal to the BC side. Find the perimeter of the trapezoid if its side is 4 cm.

The acute angles of the trapezoid are 60, and since CD is parallel to BF, then the angle AFB = CDF = 60 as the angles at the intersection of parallel lines CD and BF of the secant AD are corresponding. Then in the triangle ABF two angles are equal to 60, which means that the equilateral triangle AB = BF = FA = 4 cm.

The quadrilateral BCDF is a parallelogram, since its opposite sides are parallel, and since, by condition, BC = BF, then this parallelogram is a rhombus. Then BC = CD = DF = BF = 4 cm.

Base length АD = AF + DF = 4 + 4 = 8 cm.

Determine the perimeter of the trapezoid. P = 4 + 4 + 4 + 8 = 20 cm.

Answer: The perimeter of the trapezoid is 20 cm.



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