how do I find the perimeter of inscribed polygons?

Question

How do I find the perimeter if an octagon that is inscribed in a circle with a radius of 6?

Answer 1

You would need much more info if it is an irregular octagon. But if it is a regular octagon, matters are much simpler.

Here the octagon is divided into 8 congruent triangles eachhave a side of the octagon opposite a 45 degree angle which is formed y two radii of the circle.

So use law of cosines :
c^2 = a^2 +b^2 -2ab cos x
c^2 = 6^2 + 6^2 - 2*6*6cos45
c^2 = 36 +36 - 72(.707) = 21.096
c = =4.593
So perimeter = 8*4.593=36.74