A circle of radius 3 is inscribed in a rectangular trapezoid, the large side is 8, find the perimeter.

| March 2, 2021 | education

Formula for determining the perimeter:
P = AB + BC + AD + CD.
To solve the problem, we use the properties of a rectangular trapezoid and an inscribed circle:
1) the sum of the bases of the trapezoid is equal to the sum of the sides, that is, in this case AB + CD = AD + BC, while the formula for calculating the perimeter will take the form: P = 2 * (AB + CD);
2) the height of a rectangular trapezoid is equal to its smaller lateral side and is equal to the diameter of the inscribed circle, therefore, the smaller lateral side is equal to the diameter of the inscribed circle, that is, in our case AB = d = 2 * r = 3 * 2 = 6.
Substitute the found values ​​of the sides into the perimeter formula:
P = 2 * (AB + CD) = 2 * (8 + 6) = 2 * 14 = 28.

Answer: the perimeter of the rectangular trapezoid and the inscribed circle is 28 units.



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