Question

i need to know the formula and the answer but i can’t figure it out

Answer 1

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:

$A=\frac{\theta}{360\degree}\pi r^2$

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

$l=2\pi r\cdot\frac{\theta}{360}$

But we must add the radius 2 times, therefore the perimeter is

$\begin{gathered} p=2r+2\pi r\cdot\frac{\theta}{360} \\ \\ p=2r\mleft(1+\frac{\pi\cdot\theta}{360}\mright) \end{gathered}$

Therefore, the formulas are:

Area of a sector:

$A=\frac{\theta}{360\degree}\pi r^2$

Perimeter of a sector

$p=2r+2\pi r\cdot\frac{\theta}{360}$

Attention! all formulas in degrees, so θ must be in degrees