Multiple choice

The difference between the areas of the circumcircle and incircle of a regular polygon of n sides with each side of length 2a is.

  1. 2pna2

  2. pna2

  3. (2n+1)pa2

  4. pa2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a regular polygon of n sides with side length 2a, the difference between circumcircle area and incircle area equals pi*a^2. The circumcircle radius R = a/sin(pi/n) and incircle radius r = a*cos(pi/n)/sin(pi/n). The difference pi(R^2 - r^2) simplifies to pi*a^2 through trigonometric identity.

Keep practicing — related questions