Determine the value of the radius.

\(\displaystyle{r}=\frac{{d}}{{2}}=\frac{{12}}{{2}}={6}\)

Determine the area of the sector.

\(\displaystyle{A}=\frac{{N}}{{360}}{\left(π{r}^{{2}}\right)}\) Write the formula for area of a sector

\(\displaystyle{A}=\frac{{110}}{{360}}{\left({3.14}\right)}{\left({6}^{{2}}\right)}\) Substitute the values

\(\displaystyle{A}=\frac{{11}}{{360}}{\left({3.14}\right)}{\left({36}\right)}\) Evaluate the exponent

\(\displaystyle{A}=\frac{{11}}{{36}}{\left({3.14}\right)}{\left({36}\right)}\) Simplify the fraction

A ~ 34.54 Multiply the values.

\(\displaystyle{r}=\frac{{d}}{{2}}=\frac{{12}}{{2}}={6}\)

Determine the area of the sector.

\(\displaystyle{A}=\frac{{N}}{{360}}{\left(π{r}^{{2}}\right)}\) Write the formula for area of a sector

\(\displaystyle{A}=\frac{{110}}{{360}}{\left({3.14}\right)}{\left({6}^{{2}}\right)}\) Substitute the values

\(\displaystyle{A}=\frac{{11}}{{360}}{\left({3.14}\right)}{\left({36}\right)}\) Evaluate the exponent

\(\displaystyle{A}=\frac{{11}}{{36}}{\left({3.14}\right)}{\left({36}\right)}\) Simplify the fraction

A ~ 34.54 Multiply the values.