One important thing here is to realize that the angle is in degrees, and not radians, it changes completely the formula.
For the area of a sector we have:
[tex]A=\frac{\theta}{360\degree}\pi r^2[/tex]
Where "θ" is the angle in degrees
And for the perimeter, we have the length of the arc, plus 2 times the radius, the length of the arch using degrees is
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]
But we must add the radius 2 times, therefore the perimeter is
[tex]\begin{gathered} p=2r+2\pi r\cdot\frac{\theta}{360} \\ \\ p=2r\mleft(1+\frac{\pi\cdot\theta}{360}\mright) \end{gathered}[/tex]
Therefore, the formulas are:
Area of a sector:
[tex]A=\frac{\theta}{360\degree}\pi r^2[/tex]
Perimeter of a sector
[tex]p=2r+2\pi r\cdot\frac{\theta}{360}[/tex]
Attention! all formulas in degrees, so θ must be in degrees
