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Perimeter and Area of a Rectangle by John Ulbright

Perimeter and Area of a Rectangle by John Ulbright
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2016-03-16 00:21
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation of the perimeter and area of a rectangle. Key mathematical concepts include the formulas for area and perimeter. Using GeoGebra commands such as Polygon, Sequence, and Rotate, the example dynamically shows how changes in the dimensions of the rectangle affect its perimeter and area. Suitable for middle school and above students learning geometry and basic mathematical concepts.

GeoGebra Commands & Parameters

  1. Sort({x(A), x(B), x(C), x(D)}) → xvalues
  2. Sort({y(A), y(B), y(C), y(D)}) → yvalues
  3. Polygon(A, D, B, C) → poly1, a, d, b, c
  4. Sequence(Point[{xmin + c - i, ymin}], i, 1, c) → list8
  5. Sequence(Point[{xmin, ymin + i}], i, 0, a) → list5
  6. Sequence(Rotate[Point[{xmin + c, ymin + a - i}], (permtimer * ((-π)) / 2), (xmin + c, ymin)], i, 1, a) → list7
  7. Rotate(list5, (permtimer * ((-π)) / 2), list7(a)) → list12
  8. Sequence(Rotate[Point[{xmin + i, ymin + a}], (permtimer * ((-π)) / 2), list7(a)], i, 1, c) → list6
  9. Rotate(list12, (permtimer * ((-π)) / 2), list6(c)) → list13
  10. Rotate(list13, (permtimer * ((-π)) / 2), F) → list14
  11. Rotate(list6, (permtimer * ((-π)) / 2), list6(c)) → list11
  12. Sequence(Point[{Min[xvalues] + i, Min[yvalues] - 4}], i, 0, Area - 1) → arealist
  13. Flatten(Sequence[Sequence[Point[{Min[xvalues] + i, Min[yvalues] + j}], i, 0, c - 1], j, 0, a - 1]) → list1
  14. Sequence((list1(i) * (1 - areatimer)) + (arealist(i) * areatimer), i, 1, Area) → list2
  15. Sequence(Polygon[list2(i), list2(i) + (1, 0), 4], i, 1, Area) → list3
  16. Sequence(Polygon[arealist(i), arealist(i) + (1, 0), 4], i, 1, Area) → list4
  17. Sequence(Text[i, arealist(i) + (0.1, 0.2)], i, 1, Area) → areanumbers
  18. Flatten({Reverse[list8], Reverse[list7], Reverse[list11], Reverse[list14]}) → list9
  19. Sequence(Point[{Min[xvalues] + i, Min[yvalues] - 2}], i, 0, perm) → permlist
  20. Sequence((permlist(i) * permmover) + (list9(i) * (1 - permmover)), i, 1, Length[list9]) → list10
  21. Sequence(Segment[list10(i), list10(i + 1)], i, 1, perm) → list15
  22. Max(a + 1, ((R - L) * 17.4 / 32) + BOT) → T

AI Drawing Prompt Reference

Draw a rectangle and dynamically show changes in its perimeter and area. First, create four vertices A, B, C, and D, then use these vertices to draw a rectangle. Next, use rotation to dynamically change the rectangle's size while calculating and displaying its perimeter and area.
The prompt above was compiled from the original drawing commands and is for reference only.