SOLUTION: A regular octagon is inscribed inside a circle. The circle has a radius of 10 units.
A: What is the approximate measure of the perimeter of the octagon?
B: What is the approx
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Question 1106937: A regular octagon is inscribed inside a circle. The circle has a radius of 10 units.
A: What is the approximate measure of the perimeter of the octagon?
B: What is the approximate area of the octagon?
Choose only one answer each for parts A and B.
A: 76.5
A: 73.9
A: 61.2
A: 92.4
B: 283
B: 142
B: 353
B: 341
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a regular octagon has eight equal sides, let x be the length of one of the sides
:
we use the law of cosines
:
x^2 = 10^2 + 10^2 - 2 * 10 * 10 * cos(45) = 58.5786
x = sqrt(58.5786) = 7.6537
Perimeter of octagon = 8 * 7.6537 = 61.2296
A: 61.2
:
Note 360/8 = 45 degrees is one of the eight angles of eight isosceles triangles formed by the eight radii of the circle
:
Area of one of the isosceles triangles = (1/2) * 10^2 * sin(45) = 35.3553
Area of octagon = 8 * 35.3553 = 282.8424
B: 283
:
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