The perimeter of an isosceles trapezoid circumscribed around a circle is 44.
| September 19, 2021 | education
The perimeter of an isosceles trapezoid circumscribed around a circle is 44. Find the area of the trapezoid if the radius of the circle is 5.
Since a circle is inscribed in the trapezoid, the sum of the lengths of the bases of the trapezoid is equal to the sum of the lengths of its lateral sides.
AB + CD = BC + AD = Ravsd / 2 = 44/2 = 22 cm.
The height BH of the trapezoid is equal to the diameter of the inscribed circle. BH = 2 * R = 2 * 5 = 10 cm.
Determine the area of the trapezoid.
Savsd = (BC + AD) * BН / 2 = 22 * 10/2 = 110 cm2.
Answer: The area of the trapezoid is 110 cm2.
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