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Area and Perimeter Exploration

Area and Perimeter Exploration
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2017-01-06 05:34
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the exploration of the area and perimeter of polygons through geometric construction. Key mathematical concepts include polygons, segments, circles, angles, etc. It uses commands like Point, PolyLine, Polygon, Segment, etc., in GeoGebra. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Point(Segment[Intersect[a, x = 1], Intersect[a, y = 1]]) → P
  2. PolyLine(O, A, P, B, O) → b
  3. Intersect(Segment[A, P], Segment[Q, Q_2]) → C
  4. Polygon(O, A, C, Q_2) → poly1, o, a_1, c, q_2
  5. Segment(Q_2, C) → e
  6. Segment(C, Q) → f
  7. LineBisector(Q_2, C) → k
  8. LineBisector(B, Q) → l
  9. Intersect(k, l) → I
  10. Rotate(A, (90° * t), I) → A'_1
  11. Rotate(Q_1, (90° * t), I) → J
  12. Rotate(Q, (90° * t), I) → Q'_1
  13. Rotate(C, (90° * t), I) → C'_1
  14. Polygon(A'_1, J, Q'_1, C'_1) → poly3, a'_1, j_1, q'_1, c'_1
  15. Intersect(Segment[B, P], Segment[Q, Q_1]) → D
  16. Polygon(O, Q_1, D, B) → poly2, o_1, q_1, d, b_1
  17. LineBisector(D, Q_1) → g
  18. LineBisector(Q, A) → h
  19. Intersect(h, g) → E
  20. Rotate(B, (-90° * t), E) → B'
  21. Rotate(D, (-90° * t), E) → D'
  22. Rotate(Q, (-90° * t), E) → Q'
  23. Rotate(Q_2, (-90° * t), E) → F
  24. Polygon(B', D', Q', F) → poly4, b', d', q', f_1