Find the radius of the inscribed circle in an isosceles trapezoid with a base of 12 cm and a perimeter of 32 cm.

From the condition, we know that the trapezoid given to us is isosceles with a base of 12 cm, and the perimeter of the trapezoid is also known – 32 cm. And we need to find the radius of the inscribed circle in this trapezoid.
Recall the property of a trapezoid, if a circle is inscribed in a trapezoid, then the sum of the base is equal to the sum of the sides of the trapezoid.
Based on this, we can find the length of the second base:
32 cm / 2 = 16 cm.
16 – 12 = 4 cm length of the second base.
Let’s apply the formula to find the radius of the inscribed circle:
r = √ (c * d) / 2;
The radius of the inscribed circle is equal to half the square root of the product of the bases.
It remains for us to substitute the values ​​and calculate:
r = √ (12 * 4) / 2 = 4√3 / 2 = 2√3 cm.