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矩形面积与几何构造演示

矩形面积与几何构造演示
几何画板及绘图内容加载中，请稍等……
2012-02-22 19:36
多边形解析几何积分几何作图滑块动画
所属专题 Area, Surface Area, Volume--Nets
①本范例通过GeoGebra动态几何环境，直观演示了矩形面积的计算与相关几何构造，包括点、线段、圆、垂线、多边形等元素的组合。②核心数学概念涉及矩形面积公式、几何作图、以及通过中点、垂线等构造辅助线来研究面积关系，同时可能关联到定积分、中位线等统计特征（原标签提及）。③作图要点：从构造摘要可见，使用了Point（点）、Segment（线段）、Circle（圆）、OrthogonalLine（垂线）、Intersect（交点）、Polygon（多边形）、Midpoint（中点）等GeoGebra命令，构建了多个对象如Base、Height、A、B、C、D、E、F、G等，形成完整的矩形及其辅助图形。④适合学段：适用于初中至高中阶段，用于几何教学、面积概念理解，以及动态探索矩形性质与相关数学关系，也可作为教师演示工具或学生自主探究的素材。

GeoGebra 命令及参数

  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