Volumes and Surface Areas of Similar Cuboids by Dan Dale

GeoGebra Commands & Parameters

1. Polygon(A, B, C, D) → poly1, a, b, c, d
2. Prism(poly1, E) → e, F, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH, edgeAE
3. Point(Segment[A' + (0, 0, h), A' + (0, 0, (2 * h))]) → E'
4. Polygon(A', B', C', D') → poly2, a', b', c', d'
5. Prism(poly2, E') → f, F', edgeB'I, edgeC'J, edgeD'K, edgeE'I, edgeIJ, edgeJK, edgeE'K, G', H', faceA'B'IE', faceB'C'JI, faceC'D'KJ, faceA'D'KE', faceE'IJK, edgeA'E'
6. Segment(I, J) → g
7. Point(g) → K
8. Rotate(faceABFE, ((t * 90))°, a) → faceABFE'
9. Rotate(faceBCGF, ((t * 90))°, b) → faceBCGF'
10. Rotate(faceCDHG, ((t * 90))°, c) → faceCDHG'
11. Rotate(faceADHE, ((t * 90))°, d) → faceADHE'
12. Rotate(E, ((t * 90))°, a) → E'_1
13. Rotate(F, ((t * 90))°, a) → F'_1
14. Rotate(Rotate[faceEFGH, ((t * 90))°, a], ((t * 90))°, Segment[E'_1, F'_1]) → poly3
15. Rotate(faceA'B'IE', ((t * 90))°, a') → faceA'B'IE''
16. Rotate(faceB'C'JI, ((t * 90))°, b') → faceB'C'JI'
17. Rotate(faceC'D'KJ, ((t * 90))°, c') → faceC'D'KJ'
18. Rotate(faceA'D'KE', ((t * 90))°, d') → faceA'D'KE''
19. Rotate(E', ((t * 90))°, a') → E''
20. Rotate(F', ((t * 90))°, a') → F''
21. Rotate(Rotate[faceE'IJK, ((t * 90))°, a'], ((t * 90))°, Segment[E'', F'']) → poly4
22. Rotate(Segment[Midpoint[B', C'], Midpoint[F', G']], ((t * 90))°, b') → j
23. Rotate(Segment[Midpoint[B', F'], Midpoint[C', G']], ((t * 90))°, b') → i
24. Rotate(Segment[Midpoint[A', B'], Midpoint[E', F']], ((t * 90))°, a') → m
25. Rotate(Segment[Midpoint[A', E'], Midpoint[B', F']], ((t * 90))°, a') → n
26. Rotate(Segment[Midpoint[C', D'], Midpoint[G', H']], ((t * 90))°, c') → p
27. Rotate(Segment[Midpoint[C', G'], Midpoint[D', H']], ((t * 90))°, c') → q
28. Rotate(Segment[Midpoint[A', E'], Midpoint[D', H']], ((t * 90))°, d') → r
29. Rotate(Segment[Midpoint[A', D'], Midpoint[E', H']], ((t * 90))°, d') → s
30. Rotate(Rotate[Segment[Midpoint[E', F'], Midpoint[G', H']], ((t * 90))°, a'], ((t * 90))°, Segment[E'', F'']) → a_1
31. Rotate(Rotate[Segment[Midpoint[E', H'], Midpoint[G', F']], ((t * 90))°, a'], ((t * 90))°, Segment[E'', F'']) → b_1
32. Segment(Midpoint[A', B'], Midpoint[C', D']) → c_1
33. Segment(Midpoint[A', D'], Midpoint[C', B']) → d_1
34. Segment(Midpoint[F', C'], Midpoint[E', D']) → e_1
35. Segment(Midpoint[F', A'], Midpoint[C', H']) → f_1
36. Intersect(Line[E, E'], z = 0) → L
37. Segment(L, E) → g_1
38. Segment(L, H) → i_1
39. Segment(L, F) → k_1
40. Segment(L, G) → m_1
41. Segment(H, H') → j_1
42. Segment(G, G') → n_1
43. Segment(E, E') → h_1
44. Segment(F, F') → l_1
45. Segment(L, A) → p_1
46. Segment(A, A') → q_1
47. Segment(L, B) → r_1
48. Segment(B, B') → s_1
49. Segment(L, C) → t_1
50. Segment(C, C') → a_2
51. Segment(L, D) → b_2
52. Segment(D, D') → c_2
53. Vector(E' + (0, 0, 0.3), E' + (0, 0, 1.3)) → u
54. Segment(Midpoint[A', C'], Midpoint[E', G']) → d_2