In an isosceles trapezoid, one of the corners is 60 degrees, the side is 8 cm and the smaller base is 7 cm.

univerkov | February 21, 2021 | education

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

1. A, B, C, D – the tops of the trapezoid. AB = 8 centimeters. DK – height to the base of AD. ∠А = 60 °.

Smaller base BC = 7 centimeters. ME – middle line.

2. AK: AB = cosine ∠A = 60 ° = 1/2.

AK = AB x 1/2 = 8 x 1/3 = 4 centimeters.

3. According to the properties of an isosceles trapezoid, the segment AK = (AD – BC) / 2.

AD – BC = 4 x 2 = 8 centimeters.

AD = 8 + BC = 8 + 7 = 15 centimeters.

4. ME = (AD + BC) / 2 = (15 + 7): 2 = 11 centimeters.

Answer: The middle line of the trapezoid ABCD is 11 centimeters.

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