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Rectangle Area Formula Investigation

Rectangle Area Formula Investigation
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2013-08-03 04:11
PolygonCoordinate GeometryGeometric Construction
In collections Area Formulas Area Formulas Defining Areas for 2D Shapes
This example demonstrates how to explore the area formula for rectangles through dynamic geometry. It involves core math concepts like the area of geometric shapes, the relationship between length and width in rectangles, and the derivation of mathematical formulas. The construction uses GeoGebra commands/objects such as Point, Segment, Circle, OrthogonalLine, Intersect, Polygon, and Midpoint. Suitable for middle school students and above for learning geometric area formulas or as a teaching demonstration tool.

GeoGebra Commands & Parameters

  1. Point(Circle[A, Base]) → B
  2. Segment(A, B) → b
  3. Point(Circle[A, Height]) → C
  4. Segment(A, C) → d
  5. Circle(A, C) → e
  6. OrthogonalLine(A, b) → f
  7. Intersect(e, f, 1) → D
  8. OrthogonalLine(B, b) → g
  9. OrthogonalLine(D, f) → h
  10. Intersect(g, h) → E
  11. Polygon(A, D, E, B) → P, a_1, d_1, e_1, b_1
  12. Midpoint(A, D) → F
  13. Midpoint(A, B) → G
  14. Point(Circle[A, 1]) → H
  15. Segment(A, H) → i
  16. Point(Circle[A, 2]) → I
  17. Segment(A, I) → j
  18. Point(Circle[A, 3]) → J
  19. Segment(A, J) → k
  20. Point(Circle[A, 4]) → K
  21. Segment(A, K) → l
  22. Point(Circle[A, 5]) → L
  23. Segment(A, L) → m
  24. Point(Circle[A, 6]) → M
  25. Segment(A, M) → n
  26. Point(Circle[A, 7]) → N
  27. Segment(A, N) → p
  28. Point(Circle[A, 8]) → O
  29. Segment(A, O) → q
  30. Point(Circle[A, 9]) → Q
  31. Segment(A, Q) → r
  32. Circle(A, H) → s
  33. Circle(A, I) → t
  34. Circle(A, J) → c_1
  35. Circle(A, K) → f_1
  36. Circle(A, L) → g_1
  37. Circle(A, M) → h_1
  38. Circle(A, N) → k_1
  39. Circle(A, O) → p_1
  40. Circle(A, Q) → q_1
  41. Intersect(s, a_1, 1) → R
  42. Intersect(t, a_1, 1) → S
  43. Intersect(c_1, a_1, 1) → T
  44. Intersect(f_1, a_1, 1) → U
  45. Intersect(g_1, a_1, 1) → V
  46. Intersect(h_1, a_1, 1) → W
  47. Intersect(k_1, a_1, 1) → Y
  48. Intersect(p_1, a_1, 1) → Z
  49. Intersect(q_1, a_1, 1) → A_1
  50. Intersect(q_1, b_1, 1) → B_1
  51. Intersect(p_1, b_1, 1) → C_1
  52. Intersect(k_1, b_1, 1) → D_1
  53. Intersect(h_1, b_1, 1) → E_1
  54. Intersect(g_1, b_1, 1) → F_1
  55. Intersect(f_1, b_1, 1) → G_1
  56. Intersect(c_1, b_1, 1) → H_1
  57. Intersect(t, b_1) → I_1,
  58. Intersect(s, b_1, 1) → J_1
  59. OrthogonalLine(R, a_1) → i_1
  60. OrthogonalLine(S, a_1) → j_1
  61. OrthogonalLine(T, a_1) → l_1
  62. OrthogonalLine(U, a_1) → m_1
  63. OrthogonalLine(V, a_1) → n_1
  64. OrthogonalLine(W, a_1) → r_1
  65. OrthogonalLine(Y, a_1) → s_1
  66. OrthogonalLine(Z, a_1) → t_1
  67. OrthogonalLine(A_1, a_1) → a_2
  68. OrthogonalLine(J_1, b_1) → b_2
  69. OrthogonalLine(I_1, b_1) → c_2
  70. OrthogonalLine(H_1, b_1) → d_2
  71. OrthogonalLine(G_1, b_1) → e_2
  72. OrthogonalLine(F_1, b_1) → f_2
  73. OrthogonalLine(E_1, b_1) → g_2
  74. OrthogonalLine(D_1, b_1) → h_2
  75. OrthogonalLine(C_1, b_1) → i_2
  76. OrthogonalLine(B_1, b_1) → j_2
  77. Intersect(b_2, d_1) → K_1
  78. Intersect(c_2, d_1) → L_1
  79. Intersect(d_2, d_1) → M_1
  80. Intersect(e_2, d_1) → N_1
  81. Intersect(f_2, d_1) → O_1
  82. Intersect(g_2, d_1) → P_1
  83. Intersect(h_2, d_1) → Q_1
  84. Intersect(i_2, d_1) → R_1
  85. Intersect(j_2, d_1) → S_1
  86. Intersect(a_2, e_1) → T_1
  87. Intersect(t_1, e_1) → U_1
  88. Intersect(s_1, e_1) → V_1
  89. Intersect(r_1, e_1) → W_1
  90. Intersect(n_1, e_1) → Y_1
  91. Intersect(m_1, e_1) → Z_1
  92. Intersect(l_1, e_1) → A_2
  93. Intersect(j_1, e_1) → B_2
  94. Intersect(i_1, e_1) → C_2
  95. Segment(J_1, K_1) → k_2
  96. Segment(I_1, L_1) → l_2
  97. Segment(H_1, M_1) → m_2
  98. Segment(G_1, N_1) → n_2
  99. Segment(F_1, O_1) → p_2
  100. Segment(E_1, P_1) → q_2
  101. Segment(D_1, Q_1) → r_2
  102. Segment(C_1, R_1) → s_2
  103. Segment(B_1, S_1) → t_2
  104. Segment(R, C_2) → a_3
  105. Segment(B_2, S) → b_3
  106. Segment(T, A_2) → c_3
  107. Segment(Z_1, U) → d_3
  108. Segment(V, Y_1) → e_3
  109. Segment(W_1, W) → f_3
  110. Segment(Y, V_1) → g_3
  111. Segment(U_1, Z) → h_3
  112. Segment(A_1, T_1) → i_3
  113. Intersect(q_1, a_1) → D_2, D_4
  114. Intersect(p_1, a_1) → E_2, E_4
  115. Intersect(k_1, a_1) → F_2, F_4
  116. Intersect(h_1, a_1) → G_2, G_4
  117. Intersect(g_1, a_1) → H_2, H_4
  118. Intersect(f_1, a_1) → I_2, I_4
  119. Intersect(c_1, a_1) → J_2, J_4
  120. Intersect(t, a_1) → K_2, K_3
  121. Intersect(c_1, b_1) → L_2, L_3
  122. Intersect(f_1, b_1) → M_2, M_3
  123. Intersect(g_1, b_1) → N_2, N_3
  124. Intersect(h_1, b_1) → O_2, O_3
  125. Intersect(k_1, b_1) → P_2, P_3
  126. Intersect(q_1, b_1) → Q_2, Q_3
  127. Intersect(p_1, b_1) → R_2, R_3
  128. OrthogonalLine(D_2, a_1) → a
  129. OrthogonalLine(E_2, a_1) → c
  130. OrthogonalLine(F_2, a_1) → j_3
  131. OrthogonalLine(G_2, a_1) → k_3
  132. OrthogonalLine(H_2, a_1) → l_3
  133. OrthogonalLine(I_2, a_1) → m_3
  134. OrthogonalLine(J_2, a_1) → n_3
  135. OrthogonalLine(K_2, a_1) → p_3
  136. OrthogonalLine(L_2, b_1) → q_3
  137. OrthogonalLine(M_2, b_1) → r_3
  138. OrthogonalLine(N_2, b_1) → s_3
  139. OrthogonalLine(O_2, b_1) → t_3
  140. OrthogonalLine(P_2, b_1) → a_4
  141. OrthogonalLine(R_2, b_1) → b_4
  142. OrthogonalLine(Q_2, b_1) → c_4
  143. Intersect(q_3, d_1) → U_2
  144. Intersect(r_3, d_1) → V_2
  145. Intersect(s_3, d_1) → W_2
  146. Intersect(t_3, d_1) → Y_2
  147. Intersect(a_4, d_1) → Z_2
  148. Intersect(b_4, d_1) → A_3
  149. Intersect(c_4, d_1) → B_3
  150. Intersect(e_1, a) → C_3
  151. Intersect(e_1, c) → D_3
  152. Intersect(e_1, j_3) → E_3
  153. Intersect(e_1, k_3) → F_3
  154. Intersect(e_1, l_3) → G_3
  155. Intersect(e_1, m_3) → H_3
  156. Intersect(e_1, n_3) → I_3
  157. Intersect(p_3, e_1) → J_3
  158. Segment(U_2, L_2) → d_4
  159. Segment(M_2, V_2) → e_4
  160. Segment(W_2, N_2) → f_4
  161. Segment(O_2, Y_2) → g_4
  162. Segment(Z_2, P_2) → h_4
  163. Segment(R_2, A_3) → i_4
  164. Segment(B_3, Q_2) → j_4
  165. Segment(J_3, K_2) → k_4
  166. Segment(J_2, I_3) → l_4
  167. Segment(H_3, I_2) → m_4
  168. Segment(H_2, G_3) → n_4
  169. Segment(F_3, G_2) → p_4
  170. Segment(F_2, E_3) → q_4
  171. Segment(D_3, E_2) → r_4
  172. Segment(D_2, C_3) → s_4

AI Drawing Prompt Reference

Draw a rectangle to explore its area formula dynamically. Start by drawing one side of the rectangle and a perpendicular line as the height. Use circles and perpendicular lines to find the vertices of the rectangle, completing its outline. Then, draw several concentric circles inside the rectangle and calculate their intersections with the sides. Finally, connect these intersection points to form multiple small rectangles, visually demonstrating the derivation of the area formula.
The prompt above was compiled from the original drawing commands and is for reference only.