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QR3-01-XT1 Area Model

QR3-01-XT1 Area Model
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2018-10-27 03:27
CalculusGeometric Construction
This example demonstrates the construction and manipulation of an area model through dynamic geometry, visually illustrating methods for calculating the area of geometric shapes. It involves core mathematical concepts such as area, quadratic equations, linear equations, calculus, dilation, integers, and special points. The construction utilizes GeoGebra commands and objects like LaTeX, polygon, text, slider, initialize, question, instructions, and area expressions. Suitable for high school mathematics education, it helps students understand the connection between geometry and algebra, enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  2. Polygon({(1, -1), (1 + r, -1), (1 + r, -1 - s), (1, -1 - s)}) → A4
  3. Polygon({(0, 0), (1, 0), (1, -1), (0, -1)}) → A1
  4. Polygon({(0, 0), (1, 0), (1, -1), (0, -1)}) → A1border
  5. Polygon({(1, 0), (1 + r, 0), (1 + r, -1), (1, -1)}) → A2
  6. Polygon({(1, 0), (1 + r, 0), (1 + r, -1), (1, -1)}) → A2border
  7. Polygon({(0, -1), (1, -1), (1, -1 - s), (0, -1 - s)}) → A3
  8. Polygon({(0, -1), (1, -1), (1, -1 - s), (0, -1 - s)}) → A3border
  9. Text("x", (0, 0.75), true, true) → labelD
  10. Polygon({(1, -1), (1 + r, -1), (1 + r, -1 - s), (1, -1 - s)}) → A4border
  11. Text("x^2", (0, -0.1), true, true) → labelA
  12. Text("\vphantom{x^2}x", (-0.75, -0.1), true, true) → labelF
  13. LaTeX(("r=" * r)) → rLabel
  14. LaTeX(("s=" * s)) → sLabel
  15. Text((("\vphantom{x^2}" * If[r ≟ 1, "", "" + r]) * "x"), (1 + (r - 1) / 2, -0.1), true, true) → labelB
  16. Text((("\vphantom{x^2}" * If[s ≟ 1, "", "" + s]) * "x"), (0, -1 - (s - 1) / 2), true, true) → labelC
  17. Text(r, (1 + (r - 1) / 2, 0.75), true, true) → labelE
  18. Text(("\vphantom{x^2}" * s), (-0.75, -1 - (s - 1) / 2), true, true) → labelG
  19. Text("\vphantom{x^2}" + ((r * s)), (1 + (r - 1) / 2, -1 - (s - 1) / 2), true, true) → labelJ