The perimeter of an isosceles trapezoid circumscribed about a circle of radius 4 is 40.
| September 29, 2021 | education
The perimeter of an isosceles trapezoid circumscribed about a circle of radius 4 is 40. Find the length of the smaller base of the trapezoid.
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 = 40/2 = 20 cm.
The height of the ВН trapezoid is equal to the diameter of the inscribed circle. BH = 2 * R = 2 * 4 = 8 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * ВН / 2 = 20 * 8/2 = 80 cm2.
Answer: The area of the trapezoid is 80 cm2.
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