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Area of 2D Shapes by Mr_Stewart_Maths

Area of 2D Shapes by Mr_Stewart_Maths
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2014-10-24 05:34
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of various 2D shapes using GeoGebra, covering core concepts like area formulas, geometric constructions, and coordinate geometry. It utilizes commands such as Polygon, Segment, Intersect, Midpoint, OrthogonalLine, Line, Point, Mirror, and Circle. Suitable for middle school and above students learning area calculations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a_1, b, c, d
  2. Segment(A, B) → e
  3. Segment(A, D) → f
  4. Polygon(B_1, C_1, A) → poly2, a_2, b_1, c_1
  5. Segment(B_1, A) → j
  6. Segment(A, C_1) → k
  7. Polygon(A, B_2, C_2, D_2) → poly3, a_3, b_2, c_2, d_2
  8. Intersect(a_3, d_2) → E
  9. Segment(B_2, E) → p
  10. Segment(E, D_2) → q
  11. Polygon(F, G, H, I) → poly4, f_1, g_1, h_1, i_1
  12. Segment(G, H) → r
  13. Segment(F, I) → s
  14. Midpoint(F, I) → J
  15. OrthogonalLine(J, i_1) → t
  16. Intersect(t, g_1) → K
  17. Segment(J, K) → d_1
  18. Polygon(R, S, T) → poly6, t_1, r_1, s_1
  19. OrthogonalLine(S, s_1) → q_1
  20. Intersect(q_1, s_1) → U
  21. Line(R, T) → e_2
  22. Intersect(q_1, e_2) → V
  23. Segment(V, S) → f_2
  24. Segment(S, U) → g_2
  25. Line(A_1, D_1) → h_2
  26. OrthogonalLine(A_1, h_2) → i_2
  27. Point(i_2) → W
  28. Mirror(W, h_2) → W'
  29. Point(h_2) → Z
  30. Polygon(W', Z, W, D_1) → poly7, w', z_1, w_1, d_3
  31. Segment(W', W) → j_2
  32. Segment(D_1, Z) → k_2
  33. Circle(E_1, F_1) → p_2
  34. Segment(F_1, E_1) → l_2
  35. Line(L, M) → e_1
  36. Line(N, e_1) → j_1
  37. Line(L, N) → k_1
  38. Line(M, k_1) → l_1
  39. Intersect(j_1, l_1) → O
  40. Polygon(L, N, O, M) → poly5, l_3, n_1, o_1, m_1
  41. Midpoint(L, N) → P
  42. OrthogonalLine(P, k_1) → p_1
  43. Intersect(l_1, p_1) → Q
  44. Segment(P, Q) → m_2
  45. Segment(M, O) → n_2
  46. Segment(R, T) → q_2
  47. Point(s_1) → G_1
  48. Point(f_2) → H_1

AI Drawing Prompt Reference

Draw a complex geometric pattern composed of multiple polygons to demonstrate area calculations for different 2D shapes. Start by creating a quadrilateral and then construct two new polygons by connecting diagonals and vertices. Inside one of the polygons, draw a line segment and find a line perpendicular to one of its sides at the midpoint. Add a circle and use mirror and rotation operations to create new shapes. Combine all these elements to form a intricate design that showcases various methods for calculating areas.
The prompt above was compiled from the original drawing commands and is for reference only.