Step-by-step explanation:
We will have the following
*First: We have that the area of a sector of a circle is given by the expression:
A = r²a/2
Here r is the radius and alpha is the central angle.
*Second: We determine the central angle as follows:
[tex]36\pi =[/tex]
(12)²a/2 ➡️ a = 36í•2/(12) ²➡️
[tex]a = \frac{1}{2} \pi[/tex]
So, the central angle has a measurement of 1/2 pi.
Third: We determine the perimeter of the sector as follows:
First: we determine the arc length with two times the radius, that is:
p = 2(12) +
[tex]6\pi[/tex]
➡️ p = 24 +
[tex]6\pi[/tex]
So, the perimeter of the sector is 24+ 6pi meters [ Approximately 43 meters].
