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Regular Polygon and Circle Area Relationship

Regular Polygon and Circle Area Relationship
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2012-04-04 07:48
CirclePolygonTrigonometryGeometric Construction
In collections Area, Surface Area, Volume--Nets
This example demonstrates the relationship between the apothem of a regular polygon and the radius of its circumcircle as the number of sides changes. Key math concepts include regular polygons, circle area, apothem, perimeter, and rotation. GeoGebra commands and objects used in construction are Intersect, Circle, Rotate, Angle, Polygon, Segment, Midpoint, Perimeter, and Circumference. Suitable for high school students to understand geometric properties and dynamic changes of regular polygons.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, radius) → c
  3. Rotate(B, a, A) → B'
  4. Angle(B, A, B') → α
  5. Polygon(B, B', NumberofSides) → poly1, c_1, F, G, H, b, d, e, f, g, h, C, D
  6. Segment(A, B) → CircleRadius
  7. Midpoint(c_1) → E
  8. Segment(A, E) → Apothem
  9. Perimeter(poly1) → perimeterpoly1
  10. Circumference(c) → circumferencec