View Full Version : How do I figure this problem out?

08-20-2005, 06:39 PM
If I have a regular octagon inside of a circle with a radius of 15.8cm. How do I find the perimeter of the octagon? I thought if I get the diameter of the circle and divide it by 8 (sides of the octagon) I would get the answer is that correct?

Holla Back

08-20-2005, 07:46 PM
Draw the circle. Draw the octagon. Draw the radius lines from the center to the corners where the octagon touches the circle.

What is the measure of each of the angles formed by the pairs of radius lines from the center?

Draw the chords between successive corners, so you now have eight triangles inside the circles. Draw the height lines for each triangle, noting that these will be perpendicular to the chords.

What is the measure of the angles at the center?

Since these sixteen triangles are right triangles with hypotenuses of length 15.8 and a known angle measure, you can use trig to find the lengths of the bases of the sixteen triangles. Double this to find the length of a chord. Multiply by eight to find the perimeter.