# A circle of radius 2.5 is inscribed in a trapezoid of area 34, find the sum of the lengths of the bases of the trapezoid

January 17, 2021 | education

| Since a circle is inscribed in the trapezoid, the diameter of this circle is the height of the trapezoid.

KH = h = 2 * R = 2 * 2.5 = 5 cm.

We apply the formula for the area of a trapezoid and express from there the sum of the dyn bases of the trapezoid.

Savsd = (AD + ВС) * KН / 2.

(BP + ВС) = 2 * Savsd / KН = 2 * 34/5 = 13.6 cm.

Answer: The sum of the lengths of the bases of the trapezoid is 13.6 cm.

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