Answer:
[tex]\boxed {\boxed {\sf a= 705.6 \ units^2 }}[/tex]
Step-by-step explanation:
Since we are given the central angle in radians, we should use this formula for the sector area:
[tex]a=\frac{1}{2}r^2 \theta[/tex]
where r is the radius and θ is the angle in radians.
The radius is 14 units and the angle is 7.2 radians.
[tex]r= 14 \ units \\\theta= 7.2[/tex]
Substitute the values into the formula.
[tex]a= \frac{1}{2} (14 \ units)^2 (7.2)[/tex]
Solve the exponent.
- (14 units)²= 14 units* 14 units =196 units²
[tex]a=\frac{ 1}{2} (196 \ units^2)(7.2)[/tex]
[tex]a=\frac{ 1}{2}(1411.2 \ units^2)[/tex]
Multiply by 1/2 or divide by 2.
[tex]a= 705.6 \ units^2[/tex]
The area of the sector is 705.6 square units.
