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Equal Perimeter and Area Triangle and Rectangle

Equal Perimeter and Area Triangle and Rectangle
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2016-01-26 04:17
TrianglePolygonCoordinate Geometry
In collections RectTri Area vs. Perimeter Drafts
This example demonstrates constructing a triangle and rectangle with equal perimeter and area. Key mathematical concepts include area calculation, geometric construction, and coordinate geometry. It uses Polygon, Area, Circle, Point, Segment, OrthogonalLine, Intersect, Perimeter, etc., in GeoGebra. Suitable for high school math education or student exploration of geometric properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Area(poly1) → areaT
  3. Circle(D, perim / 2) → d
  4. Point(d) → E
  5. Segment(D, E) → e
  6. Point(e) → F
  7. OrthogonalLine(F, e) → f_1
  8. OrthogonalLine(D, e) → g
  9. Circle(F, E) → h
  10. Intersect(h, f_1, 2) → G
  11. OrthogonalLine(G, f_1) → i
  12. Intersect(g, i) → H
  13. Polygon(D, F, G, H) → poly2, d_1, f, g_1, f_2
  14. Perimeter(poly2) → k
  15. Circle(D, perim / 3) → p
  16. Intersect(p, d_1, 1) → I
  17. Circle(H, perim / 3 - f_2) → q
  18. Intersect(q, g_1, 1) → J
  19. Segment(D, I) → a_1
  20. Segment(I, F) → b_1
  21. Segment(G, J) → b_3
  22. Segment(J, H) → c_1
  23. Segment(F, G) → b_2
  24. Segment(H, D) → c_2
  25. Segment(D, F) → l
  26. Intersect(r, xAxis, 2) → K