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=(\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