Exploring the Surface Area of a Cube

Exploring the Surface Area of a Cube
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2012-11-02 16:36
① This example demonstrates the net of a cube and the step‑by‑step calculation of its surface area. ② Core mathematical concepts include solid geometry (cube), surface area, summation of polygon areas, and vector representation of edges. ③ Construction highlights: GeoGebra commands Intersect (finding intersections), Polygon (building polygonal faces), and Segment (drawing edges) are used together with numerous point objects (A, B, C, D, A', B', …) and multiple Vieleck (polygons) to assemble the six faces and their unfolded layout. ④ Suitable for middle‑school geometry lessons, high‑school solid‑geometry review, and teacher‑created instructional demos.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, C, D) → Vieleck1, a_1, b, c, d
  3. Polygon(B, B', C', C) → Vieleck2, b_1, b', c', c_1
  4. Polygon(D, C, C', D') → Vieleck3, d_1, c_2, c'_1, d'
  5. Segment(D', A') → e
  6. Segment(A', A) → f
  7. Segment(A', B') → g
  8. Polygon(E'', E, G, G'') → Vieleck4, e'', e_1, g_1, g''
  9. Polygon(G, H, H', G') → Vieleck5, g_2, h, h', g'
  10. Polygon(E, F, H, G) → Vieleck6, e_2, f_1, h_1, g_3
  11. Polygon(E, E', F', F) → Vieleck7, e_3, e', f', f_2
  12. Polygon(F, F'', H'', H) → Vieleck8, f_3, f'', h'', h_2
  13. Polygon(F'', F''', H''', H'') → Vieleck9, f''_1, f''', h''', h''_1