Answer:
The perimeter of the decagon is 80.3
Explanation:
Given:
radius = 13
polygon = decagon
To find:
The perimeter of the decagon
To determine the perimeter, we will apply the formula:
[tex]Perimeter\text{ of a polygon = side }\times\text{ number of sides}[/tex]
A decagon has 10 sides
number of sides = 10
We need to find the side length
Using an illustration:
Sum of angles at a point = 360°
Each central angle = 360/n = 360/10
Each central angle = 36°
s = side length, s/2 = half of the side length
To get the side length, we will apply sine ratio:
[tex]\begin{gathered} sin36°\text{ = }\frac{opposite}{hypotenuse} \\ opposite\text{ = s/2, hyp = 13} \\ \\ sin\text{ 18 = }\frac{\frac{s}{2}}{13} \\ sin18\text{ = }\frac{s}{26} \\ s\text{ = 26sin 18} \\ \text{s = 8.03} \end{gathered}[/tex]
The perimeter of the decagon:
[tex]\begin{gathered} Perimeter\text{ = 8.03 }\times10 \\ Perimeter\text{ = 80.3 } \end{gathered}[/tex]
