A circle is inscribed in a trapezoid with a median line of 5.6. Find the perimeter of the trapezoid.

univerkov | September 30, 2021 | education

Since the middle line of the trapezoid is equal to half the sum of the lengths of the bases of the trapezoid, then

AD + BC = 2 * KM = 2 * 5.6 = 11.2 cm.

A circle can be inscribed into a trapezoid if and only if the sum of the opposite sides of the trapezoid is equal to each other.

Then AD + BC = AB + CD = 11.2 cm.

The perimeter of the trapezoid will be:

Ravsd = (AD + BC) + (AB + CD) = 11.2 + 11.2 = 22.4 cm.

Answer: The perimeter of the trapezoid is 22.4 cm.

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