Question

A regular 2016-gon with all vertices on the unit circle is given. Find its perimeter, as a decimal to the nearest hundredth. (I have been stuck on this problem for half a hour I need help asap)

Answer 1

• 6.28 units

Explanation:

Interior angle opposite to each side of the polygon is:

• (360/2016)°

Since the circle is unit circle, its radius is 1 unit.

Let the side is a, then as per definition of sine we have:

• sin ((360/2016)/2) = (a/2)/1
• a = 2 sin (180/2016)°
• a = 0.00311665811

The perimeter is:

• P = 2016a = 2016(0.00311665811) ≈ 6.28 units