Answer:
[tex]113.10[/tex]
Step-by-step explanation:
The area of a sector with measure [tex]\theta[/tex] and radius [tex]r[/tex] is given by [tex]A_{sec}=r^2\pi\cdot \frac{\theta}{360^{\circ}}[/tex].
What we're given:
- [tex]r[/tex] of 12
- [tex]\theta[/tex] of [tex]90^{\circ}[/tex]
Substituting given values, we get:
[tex]A_{sec}=12^2\pi\cdot \frac{90}{360},\\\\A_{sec}=144\pi\cdot \frac{1}{4},\\\\A_{sec}\approx \boxed{113.10}[/tex]
