MathPlotAI Logo MathPlotAI

Adjustable Area Model

Adjustable Area Model
Loading the math board and drawing, please wait…
2018-08-24 01:51
PolygonFunctionCoordinate GeometrySlider AnimationGraphing
This example demonstrates the dynamic adjustment of polygon sides and vertices to illustrate area changes, involving core math concepts like polygon area calculation, multiplication principles, binomial distribution, correlation, natural numbers, bar charts, and polynomial functions. It utilizes GeoGebra commands like Polygon, Sequence, Point, and Text as per the construction summary, making it suitable for high school mathematics teaching to visually integrate functions, statistics, and geometry.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (factor1, 0), (factor1, factor2), (0, factor2)) → q1, f, g, h, i
  2. Sequence(Point[{i, factor2}], i, 0, factor1) → L_1
  3. Sequence(Point[{0, i}], i, 0, factor2) → L_2
  4. Point(L_1) → A
  5. Point(L_2) → B
  6. Polygon((0, 0), B, (x(A), y(B)), (x(A), 0)) → q2, j, b_1, k, l
  7. Polygon(B, (0, factor2), A, (x(A), y(B))) → q3, b_2, m, a_1, n
  8. Polygon((x(A), y(B)), A, (factor1, factor2), (factor1, y(B))) → q4, p, a_2, q, r
  9. Polygon((x(A), y(B)), (factor1, y(B)), (factor1, 0), (x(A), 0)) → q5, s, t, e, f_1
  10. Text(factor1 - x(A), Midpoint[a_2] + (0, height)) → factor1part2
  11. Text("+", A + (0, height)) → topPlus
  12. Text("+", B - (left, 0)) → leftPlus
  13. Text(y(B), Midpoint[j] - (left, 0)) → factor2part2
  14. Text(factor2 - y(B), Midpoint[b_2] - (left, 0)) → factor2part1
  15. Text(((factor2 - y(B)) * x(A)), Centroid[q3]) → area3
  16. Text((y(B) * x(A)), Centroid[q2]) → area2
  17. Text(((factor2 - y(B)) * (factor1 - x(A))), Centroid[q4]) → area4
  18. Text((y(B) * (factor1 - x(A))), Centroid[q5]) → area5
  19. Text((factor1 * factor2)) → text2
  20. Text(x(A), Midpoint[m] + (0, height)) → factor1part1
  21. Text("?", Midpoint[m] + (0, height)) → f1p1q
  22. Text("?", Midpoint[a_2] + (0, height)) → f1p2q
  23. Text("?", Midpoint[b_2] - (left, 0)) → f2p1q
  24. Text("?", Midpoint[j] - (left, 0)) → f2p2q