SOLUTION: A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units. A: What is the approximate measure of the radius (rounded to the nearest hundredth of a

Algebra ->  Surface-area -> SOLUTION: A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units. A: What is the approximate measure of the radius (rounded to the nearest hundredth of a      Log On


   

Question 1062744: A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units.
A: What is the approximate measure of the radius (rounded to the nearest hundredth of a unit)?
B: What is the approximate area of the circle (rounded to the nearest whole square unit)?
Select only one answer each for parts A and B.
A: 8.09
A: 2.63
A: 7.69
A: 4.25
B: 22
B: 186
B: 206
B: 57
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The one decagon is composed of 10 isosceles triangles.

Each base side of one isosceles triangle is 50%2F10=5%2Aunits.

Each vertex angle of one isosceles triangle is 360%2F10=36%2Adegrees and is a central angle of the circle.

Each base angle of one such isosceles triangle is %28180-36%29%2F2=72%2Adegrees.

Can you now continue with that to answer your questions?