## Task B-3.4.

A circle with a diameter of $5 \mathrm{~cm}$ is inscribed in an isosceles trapezoid with an area of $36 \mathrm{~cm}^{2}$. Determine the perimeter of the trapezoid.
## Solution.

The trapezoid is tangential, so for its sides, we have $a+c=2 b$.

The area of the trapezoid is $P=\frac{a+c}{2} \cdot v=b \cdot 2 r$.

It follows that $36=5 b, b=7.2 \text{ cm}$.

The perimeter of the trapezoid is $O=a+c+2 b=4 b=28.8 \text{ cm}$.