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Calculating Actual Area Using a Scaled Drawing

Calculating Actual Area Using a Scaled Drawing
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2023-01-27 23:56
Geometric Construction
This example demonstrates how to calculate the actual area of a room using a scaled drawing. The key mathematical concepts involve scale, area calculation, and geometric construction. The construction uses GeoGebra commands like RandomUniform, Shuffle, and Polygon to create scaled models and compute actual areas. It is suitable for students in grades 6-8 for measurement and area estimation practice.

GeoGebra Commands & Parameters

  1. RandomUniform(1, 7.999, 100) → randoms, {1.2111458055099855, 3.8089325707464563, 5.1151894953811325, 1.8012129080393011, 4.290719252613236, 7.269918569276233, 4.994934921167073, 2.465121025524579, 3.5989161314566225, 3.6597041878168883, 5.430573187771517, 6.459777621688009, 3.1371746824825455, 7.5234714341842155, 5.877088244490722, 7.142048134586424, 4.215348627598898, 2.1981203080871046, 6.736375247706555, 5.287027526045911, 6.356781347576113, 4.981015894679816, 5.1933120944582605, 3.44841019938957, 5.849167893295147, 3.450596270021063, 2.7008555723330945, 4.399712059010753, 7.318376266752407, 1.9097951062554774, 7.698504481965493, 2.6898631942030624, 1.483741288134305, 4.590544176434216, 7.531689113303022, 1.9332366424994396, 4.974170082347882, 4.550149133936972, 5.372820879999847, 1.278441011306365, 3.8306849319181615, 6.242082715575146, 2.2948830689395523, 1.5151921101156431, 5.947781646332657, 2.523707154517797, 7.407563231088848, 6.5382763593972015, 3.411215543299439, 3.3216234450002617, 3.245009817785751, 5.354041718939687, 6.254514152936212, 1.4077502182822261, 7.289349118094225, 6.488993751731399, 6.784680454825646, 7.624860515743089, 1.7611248381174593, 3.5929280132294883, 7.14218637397675, 6.580146091435655, 1.3998087455003607, 6.116611082620962, 7.316451088422276, 1.138440214593607, 3.164493264391668, 6.324316735676298, 2.3075718369986786, 5.168011585383606, 7.321807613005595, 2.42753996725284, 1.590112489798361, 7.764339752879986, 1.4999925000810712, 5.43394041903031, 1.4752592417187615, 1.682001026014297, 3.796936948877444, 3.2980272360219507, 5.341633319315523, 3.96172964585027, 2.073816050117621, 7.1562580715406785, 3.097489927242415, 3.690875382633696, 2.987771192838805, 7.908124473104278, 3.5459486370704725, 6.472850414711692, 2.3188465660085607, 5.012395622742947, 5.658282191727563, 2.6197550378769026, 5.514137881182875, 1.2800267910914782, 2.0031396189990116, 5.145178216158226, 4.285820085904344, 2.5172800492153193}
  2. Shuffle(Sequence[1, 7]) → shuffledIndices, {1, 4, 3, 5, 7, 6, 2}
  3. Shuffle({4, 5, 6, 7, 8, 9, 10, 11, 12}) → randomList2, {12, 10, 8, 4, 6, 7, 11, 9, 5}
  4. Zip((("$\text{" * A) * " }$"), A, {"\phantom{ft^2}", "ft^2", "in^2"}) → selectUnits
  5. If(caseNum ≟ 3, {1, 2, 2, 6, 6, 9, 10}, {1, 2, 3, 6, 8, 9, 10}) → roomIndexOptions
  6. Element({CellRange(B2,K2,"polygon"), CellRange(B4,K4,"polygon"), CellRange(B6,K6,"polygon")}, caseNum) → currentPlan
  7. Element(roomIndexOptions, shuffledIndices(Mod[countQuestion, Length[shuffledIndices]] + 1)) → currentRoom
  8. Element(currentPlan, currentRoom) → pulsinghighlightRoom
  9. Element({CellRange(B13,K13,"numeric"), CellRange(B14,K14,"numeric"), CellRange(B15,K15,"numeric")}, caseNum) → currentHeightIndices
  10. Element({CellRange(B9,K9,"list"), CellRange(B10,K10,"list"), CellRange(B11,K11,"list")}, caseNum) → currentBaseIndices
  11. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → scaleFeet
  12. Element({CellRange(B3,K3,"list"), CellRange(B5,K5,"list"), CellRange(B7,K7,"list")}, caseNum) → currentOffsets
  13. Element(currentOffsets, currentRoom) → measureOffsets
  14. If(Defined[Vertex[pulsinghighlightRoom, 4]], 4, 3) → numVertices
  15. Sequence(Vertex[pulsinghighlightRoom, A], A, 1, numVertices) → verticesHighlight
  16. Sequence(Segment[verticesHighlight(A) + measureOffsets(A), verticesHighlight(Mod[A, numVertices] + 1) + measureOffsets(A)], A, 1, numVertices) → measureSegments
  17. Element(currentBaseIndices, currentRoom) → baseIndices
  18. Element(currentHeightIndices, currentRoom) → heightIndex
  19. Zip(round(((A * 1 / scaleFeet) * 2), 1), A, measureSegments) → measureInches
  20. If(currentRoom < 9, (measureInches(baseIndices(1)) * measureInches(heightIndex)), If[caseNum ≟ 1, (measureInches(baseIndices(1)) * measureInches(heightIndex) / 2), ((measureInches(baseIndices(1)) + measureInches(baseIndices(2))) / 2 * measureInches(heightIndex))]) → areaInches
  21. Element(randomList2, Mod[countQuestion, 15] + 1) → randomNum2
  22. Element(roomIndexOptions, Mod[countQuestion, 20] + 1) → randomNum1
  23. Textfield(inputScaleSquareFeet) → InputBox2
  24. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  25. Corner(5) → layoutAppSize
  26. boxTool(7, 8.5, A2 + (0, 10.5)) → B2
  27. boxTool(11, 8.5, A2 + (7, 10.5)) → C2
  28. boxTool(9, 3.5, A2 + (9, 7)) → D2
  29. boxTool(0, 0, A2) → E2
  30. boxTool(9, 4.5, A2) → F2
  31. boxTool(9, 7, A2 + (9, 0)) → G2
  32. Polygon(Zip[A2 + (0, 4.5) + K, K, {(0, 0), (0, 3), (5, 3), (5, 6), (9, 6), (9, 0)}]) → H2
  33. Element(currentPlan, 1) → kitchen
  34. Element(currentPlan, 2) → living
  35. Element(currentPlan, 4) → ensuite
  36. Element(currentPlan, 8) → closet
  37. Element(currentPlan, 5) → den
  38. Element(currentPlan, 6) → bedroom
  39. Element(currentPlan, 7) → entrance
  40. boxTool(9.5, 5, A4 + (10.5, 0)) → B4
  41. boxTool(10.5, 14, A4 + (9.5, 5)) → C4
  42. boxTool(9.5, 5, A4 + (0, 5)) → H4
  43. boxTool(9.5, 9, A4 + (0, 10)) → G4
  44. boxTool(6, 5, A4) → D4
  45. boxTool(0, 0, A4) → F4
  46. Element(currentPlan, 9) → upperDeck
  47. Element(currentPlan, 3) → bath
  48. Textfield(inputActual) → InputBox3
  49. If(showDimensions, {192 / 255, 192 / 255, 192 / 255}, {77 / 255, 77 / 255, 77 / 255}) → planColor
  50. boxTool(5, 3, A2 + (0, 7.5)) → I2
  51. boxTool(4.5, 5, A4 + (6, 0)) → I4
  52. If(doubleInchScale, 2, 1) → showScaleInches
  53. If(doubleInchScale, (2 * scaleFeet), scaleFeet) → showScaleFeet
  54. Polygon({A2 + (18, 8), A2 + (26, 8), A2 + (18, 19)}) → J2
  55. Polygon({A2 + (26, 8), A2 + (26, 19), A2 + (18, 19)}) → K2
  56. Polygon({A4 + (20, 9), A4 + (25, 5), A4 + (25, 19), A4 + (20, 19)}) → J4
  57. Polygon({A4 + (20, 0), A4 + (25, 0), A4 + (25, 5), A4 + (20, 9)}) → K4
  58. Element(currentPlan, 10) → lowerDeck
  59. boxTool(6, 8, A6 + (10, 0)) → B6
  60. boxTool(13, 10, A6 + (3, 8)) → C6
  61. boxTool(8, 4.5, A6 + (16, 0)) → D6
  62. boxTool(0, 0, A6) → E6
  63. boxTool(8, 6.5, A6 + (16, 11.5)) → F6
  64. boxTool(10, 8, A6) → G6
  65. Polygon(Zip[A6 + (16, 4.5) + K, K, {(0, 0), (0, 7), (7, 7), (7, 2), (3, 2), (3, 0)}]) → H6
  66. boxTool(5, 2, A6 + (19, 4.5)) → I6
  67. Polygon({A6 + (0, 8), A6 + (3, 8), A6 + (3, 18), A6 + (-5, 18)}) → J6
  68. Polygon({A6 + (-5, 0), A6, A6 + (0, 8), A6 + (-5, 18)}) → K6
  69. boxTool(0, 0, A4) → E4
  70. Sequence(If[displayFractions, FractionText[measureInches(A)], ("\vphantom{\frac{1}{2}}" * measureInches(A))], A, 1, numVertices) → allMeasuresLatex
  71. Zip(Text[(("" * A) * "~in"), Midpoint[B] - (2.8 * UnitOrthogonalVector[B]), false, true, 0, 0], A, allMeasuresLatex, B, measureSegments) → measureLabels

AI Drawing Prompt Reference

Draw a scaled drawing of a room with multiple room outlines, such as kitchen, living room, and bedroom. Include a boundary box and measurement segments, with scale ratio and actual area labels. Construction order: draw room outlines first, then add boundary box and measurement segments, finally calculate and label the area.
The prompt above was compiled from the original drawing commands and is for reference only.