In an isosceles trapezoid, one of the angles is 60 °, the lateral side is 8 cm, and the smaller base is 7 cm

| May 5, 2021 | education

In an isosceles trapezoid, one of the angles is 60 °, the lateral side is 8 cm, and the smaller base is 7 cm. Find the midline of the trapezoid.

Let’s draw from vertices В and С heights ВK and CH, which on the basis of АD will cut off the same segments AK = DH, since the trapezoid is isosceles.

Consider a right-angled triangle ABK, in which the angle A = 60, the angle K = 90, then the angle B = 180 – 90 – 60 = 30.

The AK leg lies opposite an angle of 30, and therefore is equal to half the length of the hypotenuse AB. AK = AB / 2 = 8/2 = 4 cm.

Then DH = AK = 4 cm, and AD = AK + KH + DH = 4 + 7 + 4 = 15 cm.

The middle line of a trapezoid is equal to half the sum of the lengths of the bases of the trapezium

MR = BC + AD / 2 = (7 + 15) / 2 = 11 cm.

Answer: The middle line of the trapezoid is 11 cm.

 



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