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Surface Area of Rectangular Prisms by Duane Habecker

Surface Area of Rectangular Prisms by Duane Habecker
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2012-08-09 05:09
PolygonVectorSolid GeometryTransformationGeometric Construction
In collections Surface Area and Volume of basic figures Surface Area and Volume of basic figures Surface Area and Volume of basic figures surface nets
① This example demonstrates the net of a rectangular prism, visually showing how to compute its surface area. ② Core math concepts include solid geometry of rectangular prisms, the surface area formula, and the correspondence between the 3‑D solid and its 2‑D net. ③ Construction highlights: the applet uses Vector, Translate, Polygon, Line, Intersect, and Midpoint commands together with parameters length, width, height and points A, B, C, D, E, F, G to build the six faces and arrange them as a net. ④ Suitable for middle‑school (grades 7‑9) solid geometry lessons, as well as high‑school review or geometric construction practice.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → v
  3. Vector(A, D) → w
  4. Translate(E, Vector[height * u]) → E'
  5. Vector(E, E') → z
  6. Translate(E, Vector[width * w]) → E'_1
  7. Translate(E, Vector[length * v]) → E'_2
  8. Translate(E'_2, Vector[height * u]) → F
  9. Translate(E'_1, Vector[height * u]) → G
  10. Polygon(F, E'_2, E, E') → poly1, f, e'_2, e, e'
  11. Polygon(E, E'_1, G, E') → poly2, e_1, e'_1, g, e'_3
  12. Line(F, g) → d
  13. Line(G, e') → h
  14. Intersect(d, h) → H
  15. Polygon(F, E', G, H) → poly3, f_1, e'_4, g_1, h_1
  16. Polygon(J, I, K, L) → poly4, j, i, k, l
  17. Polygon(N, J, I, M) → poly5, n, j_1, i_1, m
  18. Polygon(N, P, O, M) → poly6, n_1, p, o, m_1
  19. Polygon(Q, R, N, J) → poly7, q, r, n_2, j_2
  20. Polygon(T, S, I, M) → poly8, t, s, i_2, m_2
  21. Polygon(V, U, O, P) → poly9, v_1, u_1, o_1, p_1
  22. Midpoint(e'_2) → W
  23. Midpoint(e_1) → Z
  24. Midpoint(e'_1) → A_1
  25. Midpoint(v_1) → B_1
  26. Midpoint(u_1) → C_1
  27. Midpoint(o) → D_1
  28. Midpoint(m_2) → E_1
  29. Midpoint(t) → F_1

AI Drawing Prompt Reference

Create a net of a rectangular prism showing how its six faces unfold into a two‑dimensional layout. Begin with a rectangular base, then attach a side rectangle of the same height and width to one edge, and another rectangle of height and length to an adjacent edge. Continue adding the remaining faces so they form a cross‑shaped arrangement: a central rectangle with four surrounding rectangles and one attached to one of them. Label the dimensions for length, width, and height to illustrate the proportions. Ensure each face is clearly outlined and positioned to demonstrate the correspondence between the 3‑D solid and its 2‑D net, suitable for teaching surface area concepts.
The prompt above was compiled from the original drawing commands and is for reference only.