Approximate area 1

Geometry Level 2

A regular polygon has 2018 sides and perimeter 1. What is its area?(EDIT: I am sorry for the incorrect alternatives to my previous question related to this one. Thanks for the reports.)

2.95E-2 1.95E-2 7.95E-2 8.95E-2

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1 solution

Steven Chase
Aug 18, 2018

A regular polygon with 2018 sides can be closely approximated as a circle.

Perimeter (circumference):

2 π r = 1 r = 1 2 π \large{2 \pi r = 1 \\ r = \frac{1}{2 \pi}}

Area:

A = π r 2 = 1 4 π 0.07958 \large{A = \pi r^2 = \frac{1}{4 \pi} \approx 0.07958}

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