A rectangular trapezoid is described near the circle, find the sides of the trapezoid if its perimeter

| June 14, 2021 | education

A rectangular trapezoid is described near the circle, find the sides of the trapezoid if its perimeter is 54 cm and the radius is 6 cm.

The length of the smaller lateral side of the trapezoid is equal to the diameter of the inscribed circle.

AB = 2 * R = 2 * 6 = 12 cm.

Since a circle is inscribed in a trapezoid, the sums of the lengths of its opposite sides are equal. AB + CD = BC + AD = Ravsd / 2 = 54/2 = 27 cm.

Then CD = 27 – AB = 27 – 12 = 15 cm.

Let’s build the height of the CH. ABCH is a rectangle, then BC = AH.

By the Pythagorean theorem, DH ^ 2 = CD ^ 2 – CH ^ 2 = 225 – 144 = 81.DH = 9 cm.

Then BC + AH + 9 = 27 cm.

BC + AH = 27 – 9 = 18 cm.

BC = AH = 18/2 = 9 cm.

AD = AH + DH = 18 cm.

Answer: The sides of the trapezoid are equal, 12 cm, 9 cm, 15 cm, 18 cm.



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