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Ratios of Areas of Hexagons

Ratios of Areas of Hexagons
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2019-04-01 13:44
PolygonTrigonometryGeometric Construction
This example demonstrates the ratio of areas of hexagons. Key mathematical concepts include geometric transformations, trigonometric functions, and geometric means. Using GeoGebra commands such as Polygon, LineBisector, and Intersect, hexagons are constructed and their area ratios are calculated. Suitable for high school geometry and trigonometry courses.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, E
  2. LineBisector(F, E) → l
  3. LineBisector(E, D) → m
  4. LineBisector(D, C) → n
  5. Intersect(l, j) → G
  6. Intersect(m, i) → H
  7. Intersect(n, h) → I
  8. Intersect(l, g) → J
  9. Intersect(m, f) → K
  10. Intersect(n, k) → L
  11. Intersect(l, m) → M
  12. Intersect(m, i) → N
  13. Circle(M, I) → c
  14. Polygon(K, J, 6) → poly2, p, R, q, r, s, t, a, O, P, Q
  15. Segment(G, N) → b
  16. Line(E, M) → d
  17. Intersect(d, s) → S
  18. Segment(M, S) → e
  19. OrthogonalLine(M, k) → f_1
  20. Segment(M, L) → g_1
  21. Segment(F, A) → h_1

AI Drawing Prompt Reference

Draw a regular hexagon first, then construct another regular hexagon inside it with a side length ratio of 1:2. Start by creating a regular hexagon with points A and B, then use the perpendicular bisectors of lines FE, ED, and DC to find points G, H, I, J, K, L, M, and N. Draw a circle with center M and radius MI, and then construct another regular hexagon KJL. Finally, connect the relevant points and lines to form two regular hexagons with the desired ratio.
The prompt above was compiled from the original drawing commands and is for reference only.