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Calculating Area of Composite Figures Using a Quilt Pattern

Calculating Area of Composite Figures Using a Quilt Pattern
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2022-11-16 10:14
TrianglePolygonCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of composite figures by decomposing quilt pattern shapes. Key math concepts include triangles, parallelograms, trapezoids, circles, and composite figure area calculations. GeoGebra commands like Max, Element, Append, Join, Polygon, Rotate, Flatten, Zip, Mod, TableText, and Sequence are used to construct and manipulate the shapes. Suitable for grades 6-8, this lesson helps students learn and practice area calculations for geometric figures.

GeoGebra Commands & Parameters

  1. Max({Length[data1], Length[data2], Length[data3]}) → maxRows
  2. Max(0, maxRows - 1) → numZeros
  3. Element({"", "0", "00", "000", "0000", "00000", "000000", "0000000", "00000000", "000000000", "0000000000", "00000000000"}, numZeros + 1) → zeroStr
  4. Append(Sequence["\phantom{1}", A, 1, maxRows + 1], "Total Area") → col0
  5. Join({{(("\cellcolor{" * colorPURPLE) * "}{Purple}")}, Sequence[If[A ≤ Length[data1], ("~" * data1(A)), ""], A, 1, maxRows], {(If[Sum[data1] < 10, "~", ""] * Sum[data1])}}) → col1
  6. Join({{(("\cellcolor{" * colorORANGE) * "}{Orange}")}, Sequence[If[A ≤ Length[data2], ("~" * data2(A)), ""], A, 1, maxRows], {(If[Sum[data2] < 10, "~", ""] * Sum[data2])}}) → col2
  7. Join({{(("\cellcolor{" * colorGRAY) * "}{Gray}")}, Sequence[If[A ≤ Length[data3], ("\,\,\," * data3(A)), ""], A, 1, maxRows], {(If[Sum[data3] < 10, "\,\,\,", ""] * Sum[data3])}}) → col3
  8. Polygon({(1, 7), (1, 4), (2, 3), (2, 6), (3, 7)}) → poly11
  9. Polygon({(3, 6), (6, 6), (7, 5), (7, 7), (4, 7)}) → poly12
  10. Polygon({(1, 3), (1, 1), (4, 1), (5, 2), (2, 2)}) → poly13
  11. Polygon({(5, 1), (7, 1), (7, 4), (6, 5), (6, 2)}) → poly14
  12. Polygon({(2, 5), (3, 5), (4, 4), (3, 4)}) → poly15
  13. Rotate(poly15, (3 * pi / 2), (4, 4)) → poly16
  14. Rotate(poly15, pi, (4, 4)) → poly17
  15. Polygon({(2, 5), (4, 7), (5, 7), (4, 8), (2, 6)}) → poly21
  16. Rotate(poly21, ((-pi)) / 2, (4, 4)) → poly22
  17. Rotate(poly21, (-pi), (4, 4)) → poly23
  18. Rotate(poly21, pi / 2, (4, 4)) → poly24
  19. Rotate(poly15, pi / 2, (4, 4)) → poly18
  20. Polygon({(4, 4), (4, 5), (3, 6), (3, 5)}) → poly25
  21. Rotate(poly25, ((-pi)) / 2, (4, 4)) → poly26
  22. Rotate(poly25, pi, (4, 4)) → poly27
  23. Rotate(poly25, pi / 2, (4, 4)) → poly28
  24. Polygon({(0, 4), (0, 8), (4, 8), (3, 7), (1, 7), (1, 5)}) → poly31
  25. Rotate(poly31, ((-pi)) / 2, (4, 4)) → poly32
  26. Rotate(poly31, pi, (4, 4)) → poly33
  27. Rotate(poly31, pi / 2, (4, 4)) → poly34
  28. Polygon({(2, 3), (2, 5), (3, 4)}) → poly35
  29. Rotate(poly35, ((-pi)) / 2, (4, 4)) → poly36
  30. Rotate(poly35, pi, (4, 4)) → poly37
  31. Rotate(poly35, pi / 2, (4, 4)) → poly38
  32. Polygon({(2, 5), (3, 5), (3, 6)}) → poly39
  33. Rotate(poly39, ((-pi)) / 2, (4, 4)) → poly39b
  34. Rotate(poly39, pi, (3.9816581927706727, 3.9816581927706722)) → poly39c
  35. Rotate(poly39, pi / 2, (4, 4)) → poly39d
  36. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly11, poly15, poly21, poly25, poly31, poly35, poly39}], B, 0, (3 * pi / 2), pi / 2]) → outlines
  37. Zip((("SetLayer(poly" * A) * ",4)"), A, polyNameExtensions) → cmdResetLayers
  38. Zip((("SetFixed(poly" * A) * ",true,true)"), A, polyNameExtensions) → cmdUnlockPieces
  39. Mod(outlineIndex, 7) → pieceType
  40. Element({0, 3, 0, 0, 0, 5, 0, 0}, pieceType + 1) → numSquares
  41. Element({1, 2, 2, 5, 2, 2, 2, 1}, pieceType + 1) → numTriangles
  42. Polygon({LegendAnchor, LegendAnchor + (1, 0), LegendAnchor + (1, 1), LegendAnchor + (0, 1)}) → legendSquare
  43. Polygon({LegendAnchor + (4, 0), LegendAnchor + (5, 0), LegendAnchor + (5, 1)}) → legendTriangle
  44. TableText(col0, col1, col2, col3, tableFormatStr) → dataTable
  45. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly11, poly15}], B, 0, (3 * pi / 2), pi / 2]) → color1pieces
  46. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly21, poly25}], B, 0, (3 * pi / 2), pi / 2]) → color2pieces
  47. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly31, poly35, poly39}], B, 0, (3 * pi / 2), pi / 2]) → color3Pieces
  48. Sequence(true, i, 1, 28) → allCovers
  49. Join({Sequence[Segment[AnchorA + (i, 0), AnchorA + (i, 8)], i, 1, 7], Sequence[Segment[AnchorA + (0, i), AnchorA + (8, i)], i, 1, 7]}) → quiltGrid

AI Drawing Prompt Reference

Draw a composite figure composed of various geometric shapes, including triangles, parallelograms, trapezoids, and circles. Start by drawing a heptagon, then rotate multiple small polygons around a central point to form a complex pattern. Finally, combine these shapes based on their rotation angles and types to create a complete pattern and calculate and display the area of each shape.
The prompt above was compiled from the original drawing commands and is for reference only.