Circumscribed circle - inscribed circle area formula

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SUMMARY

The discussion focuses on deriving the formula for the area difference between the circumscribed circle and the inscribed circle of a regular polygon. The formula provided is \(\frac{L^{2} \pi}{4}\), where L represents the length of each side of the polygon. This formula is applicable to any regular polygon, confirming its versatility in geometric calculations. The user successfully clarified their confusion regarding the area calculations of these circles.

PREREQUISITES
  • Understanding of regular polygon properties
  • Knowledge of circle area formulas
  • Familiarity with basic algebra
  • Concept of inscribed and circumscribed circles
NEXT STEPS
  • Research the derivation of the area formula for inscribed circles in polygons
  • Explore the properties of regular polygons and their geometric implications
  • Learn about the relationship between side length and radius in circumscribed circles
  • Investigate applications of these formulas in real-world geometric problems
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Mathematicians, geometry students, and educators looking to deepen their understanding of polygonal area calculations and the relationships between inscribed and circumscribed circles.

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I'm looking for a formula that subtracts the area of an inscribed circle of a shape from the circumscribed area of the shape. I've confused myself on this one and can't seem to figure it out.

The shape is a regular polygon (all sides and angles are equal). What should be given to "plug in" is each side is of length L and there are s sides.

Can anyone help me? Thanks!
 
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Got it!\frac{L^{2} \pi\ }{4}

Where L is the length of each side. Works for any regular polygon.Sorry, you can close this thread if you please.
 

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