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Measurement: Year 9 Maths_ Area of an Arrow

Measurement: Year 9 Maths_ Area of an Arrow
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2014-08-02 18:38
Coordinate GeometryGeometric Construction
This example demonstrates how to investigate the area of an arrow as a composite shape using an interactive tool. Key math concepts include area calculation, geometric construction, and coordinate system application. The construction involves commands/objects like Segment, Midpoint, Circle, Point, Tangent, Line, Intersect, OrthogonalLine, Polygon, and Area in GeoGebra. Suitable for Year 9 students or learners reviewing area calculations of composite figures.

GeoGebra Commands & Parameters

  1. Segment(B_1, C) → a
  2. Midpoint(a) → D
  3. Circle(D, B_1) → c
  4. Point(a) → E
  5. Circle(D, E) → d
  6. Tangent(B_1, c) → b,
  7. Line(E, b) → e
  8. Line(C, b) → f
  9. Intersect(d, a) → A_1, F
  10. Line(F, b) → g
  11. Point(b) → G
  12. Line(D, b) → i
  13. Point(b) → L
  14. Point(b) → H
  15. Segment(H, G) → h
  16. Point(h) → A
  17. OrthogonalLine(A, h) → k
  18. Point(b) → J
  19. Segment(L, J) → j
  20. Point(j) → B
  21. OrthogonalLine(B, j) → l
  22. Intersect(k, e) → M
  23. Intersect(k, i) → N
  24. Intersect(g, k) → O
  25. Intersect(k, f) → P
  26. Intersect(l, e) → Q
  27. Intersect(l, i) → R
  28. Intersect(l, g) → S
  29. Intersect(l, f) → T
  30. Segment(A, R) → m
  31. Segment(P, R) → n
  32. Segment(A, M) → p
  33. Segment(P, O) → q
  34. Segment(M, E) → r
  35. Segment(E, F) → s
  36. Segment(F, O) → t
  37. Polygon(A, M, E, D, F, O, P, R) → poly1, i_1, m_1, e_1, d_1, f_1, o, p_1, r_1
  38. Polygon(E, B_1, A, M) → Rectangle_1, e_2, b_1, i_2, m_2
  39. Polygon(F, C, P, O) → Rectangle_2, f_2, c_1, p_2, o_1
  40. Polygon(A, N, R, B) → poly4, i_3, n_1, r_2, k_1
  41. Polygon(N, P, T, R) → poly5, n_2, p_3, t_1, r_3
  42. Polygon(R, B, A) → Triangle_3, i_4, r_4, k_2
  43. Polygon(P, R, T) → Triangle_4, t_2, p_4, r_5
  44. Polygon(A, N, R) → Triangle_1, r_6, i_5, n_3
  45. Polygon(N, P, R) → Triangle_2, r_7, n_4, p_5
  46. Point(b) → I
  47. OrthogonalLine(I, b) → a_1
  48. Intersect(e, a_1) → K
  49. Intersect(g, a_1) → U
  50. Intersect(f, a_1) → V
  51. Point(b) → W
  52. OrthogonalLine(W, b) → g_1
  53. Intersect(e, g_1) → Z
  54. Intersect(g, g_1) → C_1
  55. Intersect(f, g_1) → D_1
  56. Segment(W, D_1) → h_1
  57. Segment(I, K) → j_1
  58. Segment(B_1, W) → l_1
  59. Segment(C, D_1) → q_1
  60. Segment(K, U) → s_1
  61. Segment(U, V) → a_2
  62. OrthogonalLine(B_1, b_1) → b_2
  63. Point(b_2) → E_1
  64. OrthogonalLine(E_1, b_2) → c_2
  65. Intersect(c_2, k) → F_1
  66. Point(k) → G_1
  67. OrthogonalLine(G_1, k) → d_2
  68. Intersect(d_2, l) → H_1
  69. Segment(E_1, F_1) → g_2
  70. Segment(G_1, H_1) → h_2
  71. Polygon(E, M, O, F) → Rectangle_3, e_3, m_3, o_2, f_3
  72. OrthogonalLine(R, i_4) → j_2
  73. OrthogonalLine(B, i_4) → l_2
  74. Point(l_2) → I_1
  75. OrthogonalLine(I_1, l_2) → q_2
  76. Intersect(q_2, j_2) → J_1
  77. Segment(I_1, J_1) → s_2
  78. Point(s_2) → K_1
  79. Area(Rectangle_1) → u
  80. Area(Rectangle_3) → v
  81. Area(poly1) → w
  82. Area(Triangle_1) → u_1

AI Drawing Prompt Reference

Draw an arrow shape by first sketching the base and tip, then creating two circles centered at the midpoint of the base and the tangent point, connecting the tangent point to the tip. Add auxiliary lines at intersection points, fill the enclosed areas formed by these points and lines, while keeping some lines visible to outline the arrow and its internal segments.
The prompt above was compiled from the original drawing commands and is for reference only.