MathPlotAI Logo MathPlotAI

Interactive Surface Area of a Cuboid

Interactive Surface Area of a Cuboid
Loading the math board and drawing, please wait…
2019-12-02 11:03
PolygonSolid GeometryGeometric ConstructionSlider Animation
① This GeoGebra example demonstrates the surface area of a cuboid (rectangular prism) interactively, allowing users to input length, width, and height values and observe the areas of individual faces and the total surface area update in real time. ② Core mathematical concepts include solid geometry, rectangular faces, area calculation, lateral surface area, and total surface area decomposition. ③ Construction details: Based on the construction summary, the example uses commands such as Textfield, Point, Segment, Line, Intersect, and OrthogonalLine, creating objects like l_1, h_1, b_2, multiple input boxes (inputBox1, inputBox2, etc.), and text objects (text2). Variables lb, bh, and lh represent the areas of the three distinct faces, which are summed to obtain the total surface area. ④ This resource is suitable for middle or high school students learning introductory solid geometry, as well as for teachers to illustrate the formula for the surface area of a cuboid, enhancing spatial reasoning and conceptual understanding.

GeoGebra Commands & Parameters

  1. Textfield(l_1) → inputBox1
  2. Textfield(b_2) → inputBox2
  3. Textfield(h_1) → inputBox3
  4. Textfield(l_1) → inputBox1_1
  5. Textfield(b_2) → inputBox2_1
  6. Textfield(h_1) → inputBox3_1
  7. Textfield(l_1) → inputBox1_2
  8. Textfield(b_2) → inputBox2_2
  9. Textfield(h_1) → inputBox3_2
  10. Textfield(l_1) → inputBox1_3
  11. Textfield(b_2) → inputBox2_3
  12. Textfield(h_1) → inputBox3_3
  13. Point(Circle[A, abs(l_1)]) → B
  14. Segment(A, B) → l
  15. Point(Circle[B, abs(b_2)]) → C
  16. Segment(B, C) → b
  17. Line(C, l) → d
  18. Line(A, b) → e
  19. Intersect(e, d) → D
  20. Segment(D, C) → f
  21. Segment(D, A) → g
  22. OrthogonalLine(A, l) → i
  23. OrthogonalLine(B, l) → j
  24. OrthogonalLine(D, f) → k
  25. OrthogonalLine(C, f) → m
  26. Point(Circle[A, abs(h_1)]) → E
  27. Segment(A, E) → h
  28. Point(Circle[B, abs(h_1)]) → F
  29. Segment(B, F) → p
  30. Line(E, g) → q
  31. Line(E, l) → r
  32. Line(F, b) → s
  33. Intersect(m, s) → G
  34. Intersect(q, k) → H
  35. Segment(H, G) → t
  36. Segment(F, G) → a_1
  37. Segment(E, H) → b_1
  38. Segment(C, G) → c_1
  39. Segment(H, D) → d_1
  40. Segment(E, F) → e_1
  41. Textfield(l_1) → inputBox1_4
  42. Textfield(b_2) → inputBox2_4
  43. Textfield(h_1) → inputBox3_4
  44. Textfield(l_1) → inputBox1_5
  45. Textfield(b_2) → inputBox2_5
  46. Textfield(h_1) → inputBox3_5
  47. Textfield(l_1) → inputBox1_6
  48. Textfield(b_2) → inputBox2_6
  49. Textfield(h_1) → inputBox3_6
  50. Textfield(l_1) → inputBox1_7
  51. Textfield(b_2) → inputBox2_7
  52. Textfield(h_1) → inputBox3_7
  53. Point(Circle[A_1, abs(l_1)]) → B_1
  54. Segment(A_1, B_1) → l_2
  55. Point(Circle[B_1, abs(b_2)]) → C_1
  56. Segment(B_1, C_1) → b_3
  57. Line(C_1, l_2) → d_2
  58. Line(A_1, b_3) → e_2
  59. OrthogonalLine(A_1, l_2) → i_1
  60. OrthogonalLine(B_1, l_2) → j_1
  61. Point(Circle[A_1, abs(h_1)]) → E_1
  62. Segment(A_1, E_1) → h_2
  63. Line(E_1, l_2) → r_1
  64. Textfield(l_1) → inputBox1_8
  65. Textfield(b_2) → inputBox2_8
  66. Textfield(h_1) → inputBox3_8
  67. Textfield(l_1) → inputBox1_9
  68. Textfield(b_2) → inputBox2_9
  69. Textfield(h_1) → inputBox3_9
  70. Textfield(l_1) → inputBox1_{10}
  71. Textfield(b_2) → inputBox2_{10}
  72. Textfield(h_1) → inputBox3_{10}
  73. Textfield(l_1) → inputBox1_{11}
  74. Textfield(b_2) → inputBox2_{11}
  75. Textfield(h_1) → inputBox3_{11}
  76. Point(Circle[A_2, abs(l_1)]) → B_2
  77. Segment(A_2, B_2) → l_3
  78. Point(Circle[B_2, abs(b_2)]) → C_2
  79. Segment(B_2, C_2) → b_4
  80. Line(C_2, l_3) → d_3
  81. Line(A_2, b_4) → e_3
  82. OrthogonalLine(A_2, l_3) → i_2
  83. OrthogonalLine(B_2, l_3) → j_2
  84. Point(Circle[A_2, abs(h_1)]) → E_2
  85. Segment(A_2, E_2) → h_3
  86. Line(E_2, l_3) → r_2
  87. Textfield(l_1) → inputBox1_{12}
  88. Textfield(b_2) → inputBox2_{12}
  89. Textfield(h_1) → inputBox3_{12}
  90. Textfield(l_1) → inputBox1_{13}
  91. Textfield(b_2) → inputBox2_{13}
  92. Textfield(h_1) → inputBox3_{13}
  93. Textfield(l_1) → inputBox1_{14}
  94. Textfield(b_2) → inputBox2_{14}
  95. Textfield(h_1) → inputBox3_{14}
  96. Textfield(l_1) → inputBox1_{15}
  97. Textfield(b_2) → inputBox2_{15}
  98. Textfield(h_1) → inputBox3_{15}
  99. Textfield(l_1) → inputBox1_{16}
  100. Textfield(b_2) → inputBox2_{16}
  101. Textfield(h_1) → inputBox3_{16}
  102. Textfield(l_1) → inputBox1_{17}
  103. Textfield(b_2) → inputBox2_{17}
  104. Textfield(h_1) → inputBox3_{17}
  105. Textfield(l_1) → inputBox1_{18}
  106. Textfield(b_2) → inputBox2_{18}
  107. Textfield(h_1) → inputBox3_{18}
  108. Textfield(l_1) → inputBox1_{19}
  109. Textfield(b_2) → inputBox2_{19}
  110. Textfield(h_1) → inputBox3_{19}
  111. Point(Circle[A_3, abs(l_1)]) → B_3
  112. Segment(A_3, B_3) → l_4
  113. Point(Circle[B_3, abs(b_2)]) → C_3
  114. Segment(B_3, C_3) → b_5
  115. Line(C_3, l_4) → d_4
  116. Line(A_3, b_5) → e_4
  117. OrthogonalLine(A_3, l_4) → i_3
  118. OrthogonalLine(B_3, l_4) → j_3
  119. Point(Circle[A_3, abs(h_1)]) → E_3
  120. Segment(A_3, E_3) → h_4
  121. Line(E_3, l_4) → r_3
  122. Textfield(l_1) → inputBox1_{20}
  123. Textfield(b_2) → inputBox2_{20}
  124. Textfield(h_1) → inputBox3_{20}
  125. Textfield(l_1) → inputBox1_{21}
  126. Textfield(b_2) → inputBox2_{21}
  127. Textfield(h_1) → inputBox3_{21}
  128. Textfield(l_1) → inputBox1_{22}
  129. Textfield(b_2) → inputBox2_{22}
  130. Textfield(h_1) → inputBox3_{22}
  131. Textfield(l_1) → inputBox1_{23}
  132. Textfield(b_2) → inputBox2_{23}
  133. Textfield(h_1) → inputBox3_{23}
  134. Textfield(l_1) → inputBox1_{24}
  135. Textfield(b_2) → inputBox2_{24}
  136. Textfield(h_1) → inputBox3_{24}
  137. Textfield(l_1) → inputBox1_{25}
  138. Textfield(b_2) → inputBox2_{25}
  139. Textfield(h_1) → inputBox3_{25}
  140. Textfield(l_1) → inputBox1_{26}
  141. Textfield(b_2) → inputBox2_{26}
  142. Textfield(h_1) → inputBox3_{26}
  143. Textfield(l_1) → inputBox1_{27}
  144. Textfield(b_2) → inputBox2_{27}
  145. Textfield(h_1) → inputBox3_{27}
  146. Textfield(l_1) → inputBox1_{28}
  147. Textfield(b_2) → inputBox2_{28}
  148. Textfield(h_1) → inputBox3_{28}
  149. Textfield(l_1) → inputBox1_{29}
  150. Textfield(b_2) → inputBox2_{29}
  151. Textfield(h_1) → inputBox3_{29}
  152. Textfield(l_1) → inputBox1_{30}
  153. Textfield(b_2) → inputBox2_{30}
  154. Textfield(h_1) → inputBox3_{30}
  155. Textfield(l_1) → inputBox1_{31}
  156. Textfield(b_2) → inputBox2_{31}
  157. Textfield(h_1) → inputBox3_{31}

AI Drawing Prompt Reference

Create an interactive cuboid surface area diagram. Start with a base rectangle whose length, width, and height are controlled by three input boxes. From each base vertex, draw vertical edges upward to form the top rectangle, and connect all edges. Use distinct colors or transparency for the six faces, labeling each face's area (length×width, width×height, length×height) and showing the total surface area formula nearby. The figure should update in real time as input values change, with face areas and total area updating accordingly.
The prompt above was compiled from the original drawing commands and is for reference only.