1 Answer

Chung Nguyen · Answer 1 · 2023-08-17T23:38:59+0000

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:

$A=(\theta)/(360\degree)\pi r^2$

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

$l=2\pi r\cdot(\theta)/(360)$

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

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

Therefore, the formulas are:

Area of a sector:

$A=(\theta)/(360\degree)\pi r^2$

Perimeter of a sector

$p=2r+2\pi r\cdot(\theta)/(360)$

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

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