In an isosceles trapezoid ABCD, the segment BF is parallel to the side of CD and cuts off the rhombus FBCD from it.

| September 23, 2021 | education

In an isosceles trapezoid ABCD, the segment BF is parallel to the side of CD and cuts off the rhombus FBCD from it. The acute angle of the trapezoid is 60. Find the larger base of the trapezoid if the perimeter of the FBCD rhombus is 20cm.

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.

By condition ВСDF rhombus. Since all sides of a rhombus are equal, and the perimeter is 20 cm, then BC = CD = DF = FB = 20/4 = 5 cm.Then AF = AB = 5 cm, and AD = 5 + 5 = 10 cm.

Determine the perimeter of the trapezoid. P = 5 + 5 + 5 + 10 = 25 cm.

Answer: The perimeter of the trapezoid is 25 cm.



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