Answer:
[tex]12.6\pi\:\mathrm{km^2}\:\text{or }\frac{63}{5}\pi\:\mathrm{km^2}[/tex]
Step-by-step explanation:
The area of a sector with measure [tex]\theta[/tex] in degrees is given by [tex]r^2\pi\cdot\frac{\theta}{360}[/tex], where [tex]r[/tex] is the radius of the sector.
What we're given:
- [tex]r[/tex] of 6
- [tex]\theta[/tex] of [tex]126^{\circ}[/tex]
Substituting given values, we get:
[tex]A_{sec}=6^2\pi \cdot\frac{126}{360}=\boxed{12.6\pi\:\mathrm{km^2}}[/tex]
