In an isosceles trapezoid ABCD (AB = CD), the smaller base of BC is equal to the lateral side.

| April 29, 2021 | education

In an isosceles trapezoid ABCD (AB = CD), the smaller base of BC is equal to the lateral side. The acute angle of the trapezoid is 60 degrees. Find the midline of the trapezoid if the larger base of the trapezoid is 14 m.

Let the side length AB be equal to X cm, then BC = CD = AB = X cm.

We draw from the top of an obtuse angle B to the height of the ВН. Then, in a right-angled triangle ABН, the angle ABН = 180 – 90 – 60 = 30. The leg AH lies opposite the angle 30 and is equal to half the length of AB. AH = AB / 2 = X / 2.

The segment DH is equal to the half-sum of the bases of the trapezoid.

DН = (BC + AD) / 2.

DН = (X + 14) / 2.

Then the base AD = AH + DН.

14 = X / 2 + (X +14) / 2.

28 = 2 * X + 14.

2 * X = 14.

X = AB = BC = CD = 14/2 = 7cm.

Determine the length of the midline of the trapezoid.

КР = (ВС + АD) / 2 = (7 + 14) / 2 = 21/2 = 10.5 cm.

Answer: The length of the middle line is 10.5 cm.



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