Answer :
Answer:
[tex]\boxed {\boxed {\sf a \approx207.35 \ in^2}}[/tex]
Step-by-step explanation:
Since the central angle is given in degrees, we should use this formula to find the area of the sector:
[tex]a=\frac{\theta}{360} \times \pi r^2[/tex]
The central angle is 165 degrees and the radius is 12 inches.
- θ= 165
- r= 12 in
Substitute the values into the formula.
[tex]a= \frac{165}{360} \times \pi (12 \ in)^2[/tex]
Solve the exponent.
- ( 12 in)² = 12 in * 12 in =144 in²
[tex]a= \frac{165}{360} \times \pi(144 \ in^2)[/tex]
Multiply all the numbers together.
[tex]a= 207.345115137 \ in^2[/tex]
Round to the nearest hundredth (two decimal places).
- 207.345115137
The 5 in the thousandth place (in bold above) tells us to round the 4 in the hundredth place up to a 5.
[tex]a \approx207.35 \ in^2[/tex]
The area of the sector is approximately 207.35 inches squared.