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Area of Circle Sectors

Area of Circle Sectors
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2018-12-15 22:59
CirclePolygonGeometric Construction
This example demonstrates how to divide a circle into sectors and calculate the area of each sector. Key concepts include the area formula of a circle and the calculation of sector areas. Commands used include Polygon, Circle, Point, Rotate, Segment, Midpoint, Sequence, CircleSector, etc. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (base, 0), (base, r), (0, r)) → poly1, a, b, c, d
  2. Circle(A, r) → e
  3. Point(e) → B
  4. Rotate(B, (360 * ° / n), A) → B'
  5. Segment(B, B') → dx
  6. Midpoint(dx) → C
  7. Segment(A, C) → dy
  8. Sequence(Rotate[B, ((j * 360) * ° / n), A], j, 0, n) → list1
  9. Sequence(CircleSector[A, Element[list1, j], Element[list1, j + 1]], j, 1, n, 2) → list2
  10. Sequence(CircleSector[A, Element[list1, j], Element[list1, j + 1]], j, 2, n, 2) → list3
  11. Sequence(CircleSector[((j * dx) + dx / 2, dy), ((j * dx) + 0, 0), ((j * dx) + dx, 0)], j, 0, n / 2 - 1) → list5
  12. Sequence(CircleSector[((j * dx), 0), ((j * dx) + dx / 2, dy), ((j * dx) + ((-dx)) / 2, dy)], j, 1, n / 2 - 1) → list4
  13. CircleSector((0, 0), (dx / 2, dy), (0, dy)) → wedgeS
  14. CircleSector(((n / 2 * dx) + 0, 0), ((n / 2 * dx), r), ((n / 2 * dx) - dx / 2, dy)) → wedgeE
  15. Segment(D, D') → f
  16. Midpoint(f) → E
  17. Segment(A', E) → g