Since, according to the task, there is a tangent circle inside the trapezoid, so this trapezoid is a tangent quadrilateral! Therefore, the following relation can be written:

$$a+b=c+c$$

$$8+2=2c$$

$$2c=10$$

$$c=\frac{10}{2}$$

$$c=5$$

$$c^2={\left(\frac{a-b}{2}\right)}^2+h^2$$

$$5^2={\left(\frac{8-2}{2}\right)}^2+h^2$$

$$5^2=3^2+h^2$$

$$25=9+h^2$$

$$h^2=25-9$$

$$h^2=16$$

$$h=\sqrt{16}$$

$$h=4$$

$$h=2·r$$

$$r=\frac{h}{2}=\frac{4}{2}$$

$$r=2$$

$$A=s·r$$

$$s=\frac{a+b+c+c}{2}=\frac{8+2+5+5}{2}=\frac{20}{2}$$

$$s=10$$

$$A=s·r=10·2$$