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Perimeter and Area of Polygons

Perimeter and Area of Polygons
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2020-04-19 15:07
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the perimeter and area of polygons. Key mathematical concepts include polygons, geometric construction, and coordinate geometry. Using GeoGebra commands such as Segment, Polygon, Perimeter, etc., dynamic construction of polygons and observation of changes in perimeter and area are possible. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(B, C) → e
  2. Segment(I, A) → n
  3. Segment(A, B) → d
  4. Take(listepoint, 1, a) → liste2_1
  5. Polygon(liste2_1) → poly1
  6. Centroid(poly1) → J
  7. Segment(H, If[a ≟ 8, A, I]) → k
  8. Segment(G, If[a ≟ 7, A, H]) → j
  9. Segment(F, If[a ≟ 6, A, G]) → i
  10. Segment(E, If[a ≟ 5, A, F]) → h
  11. Segment(D, If[a ≟ 4, A, E]) → g
  12. Segment(C, If[a ≟ 3, A, D]) → f
  13. Take(listeseg, 1, a) → liste1
  14. Length(liste1) → l
  15. Sequence(Sum[First[Append[0, liste1], i]], i, 1, l) → liste2
  16. Sequence(Polygon[Element[listepoint, i], Element[listepoint, i + 1], J], i, 1, ni) → l3
  17. RemoveUndefined(l3) → l4
  18. Perimeter(poly1) → b
  19. Sum(liste1) → s
  20. Sequence(Element[liste1, i], i, 1, ni - 1) → liste3
  21. Point(Element[liste1, ni], (p - Element[liste2, ni]) / Element[liste1, ni]) → P
  22. Segment(Point[Element[liste1, ni], 0], P) → c
  23. Circle(P, 2) → q
  24. Sequence(Intersect[q, Element[liste1, i]], i, 1, Length[liste1]) → liste4
  25. Sequence(Polygon[J, A, Element[listepoint, i]], i, 1, Length[liste3]) → l1
  26. Sequence(CircleSector[J, Element[listepoint, i], Element[listepoint, i + 1]], i, 1, ni - 1) → l2
  27. Polygon(liste2_1) → poly2
  28. Sum(l4) → o
  29. Polygon(Element[listepoint, a], J, Element[listepoint, 1]) → t1, m, r, j_1

AI Drawing Prompt Reference

Draw a polygon with points A, B, C, D, E, F, G, H, I, connecting these points to form a polygon and calculate its perimeter and area. First, connect points B and C, I and A, A and B, then sequentially connect point A to other points to form the polygon. Next, calculate the perimeter and area of the polygon, observing how changes in side lengths affect the perimeter and area.
The prompt above was compiled from the original drawing commands and is for reference only.