Answer:
[tex]42.5\:\mathrm{m^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 5
- [tex]\theta[/tex] of [tex]195^{\circ}[/tex]
Solving, we get:
[tex]A_{sector}=5^2\pi\cdot \frac{195}{360}=13.5416666667\pi=42.5424005174\approx \boxed{42.5\:\mathrm{m^2}}[/tex]
*Notes:
- units should be in square meters (area)
- the problem does not say whether to round or leave answers in term of pi, so you may need to adjust the answer depending on what your teacher specifically wants
