The side of an isosceles trapezoid = 6 cm. Find the midline of the trapezoid if 1 of its angle = 60 degrees, and the larger base = 3 cm.
| February 16, 2021 | education
Let’s build the height of the HВ trapezoid of AВСD.
The height of the isosceles trapezoid forms a right-angled triangle ABН in which the angle ABН = 60, then the angle ABН = (90 – 60) = 30.
The leg AH lies opposite an angle of 300, then its length is equal to half the length of the hypotenuse AB. AH = AB / 2 = 6/2 = 3 cm.Then DН = AD – AH = 9 – 3 = 6 cm.
The height of an isosceles trapezoid divides its larger base into two segments, the length of the larger of which is equal to the midline of the trapezoid. DН = KM = 6 cm.
Answer: The length of the middle line is 6 cm.
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