The formula below gives the relationship between the number of sides n , the radius r , and the length of each side l in a regular polygon. Find n , if l = 1 r .
A)n = 8
B)n = 5
C)n = 7
D)n = 6
E)n = 4

Question

The formula below gives the relationship between the number of sides n , the radius r , and the length of each side l  in a regular polygon. Find n , if  ​l ​ = 1 ​r ​.   ​
A)n = 8 
B)n = 5 
C)n = 7 
D)n = 6 
E)n = 4

Quizplus · Accepted Answer

The formula for the length of each side of a regular polygon is l = 2r sin(π/n). If l = r, then 
r = 2r sin(π/n) 
1 = 2 sin(π/n) 
sin(π/n) = 1/2 
π/n = π/6 
n = 6. Therefore, the answer is choice D, n=6.

The Formula Below Gives the Relationship Between the Number of Sides