Question

q

Answer 1

each side subtends an angle 360/5 = 72 at the center of the circle. (since it's a regular pentagon). if you construct a triangle making use of any two vertices of pentagon and the center as the third vertex, you will have an isosceles triangle with equal sides being the radii of the circle. from the triangle one can easily see that the side of the pentagon will be 2 times R sin 36. which makes the perimeter = 10 R sin 36