[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's find the Area of sector ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{ \theta}{360} \times \pi{r}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ 270}{360} \times \pi{6}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ 3}{4} \times {36}^{} \pi[/tex]
[tex]\qquad \sf \dashrightarrow \:3 \times 9 \pi[/tex]
[tex]\qquad \sf \dashrightarrow \:27\pi \: \: ft {}^{2} [/tex]