The area of a circle that is inscribed in a square of area $17\frac{9}{11}$ cm² is:

14 cm²

We know that,

Area of circle = πr²

Area of square = side²

We can write $17\frac{9}{11}$ as = $\frac{196}{11}$

side² = $\frac{196}{11}$

side = \(\frac{14}{ \sqrt {11}}\)

Here we can find that

The side of a square = Diameter of he square

radiius = \(\frac{14}{ \sqrt {11}}\) × \(\frac{1}{2}\) = \(\frac{7}{ \sqrt {11}}\) 

Area of a circle =  πr² = \(\frac{22}{7}\) × (\(\frac{7}{ \sqrt {11}}\))²

Area of a circle = 14