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Total Area Calculation

Total Area Calculation
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2019-01-29 08:06
PolygonSequenceOptimization
This example demonstrates calculating the total area of a parallelogram, trapezoid, rectangle, and triangle. Key mathematical concepts include area calculation, polygons, and straight lines. Using GeoGebra commands such as Point, Polygon, If, Segment, Sequence, etc., the example allows dynamic adjustment of parameters to observe area changes. Suitable for middle school and above students to learn area calculation and optimization problems.

GeoGebra Commands & Parameters

  1. Point({36, 0}) → parStarter
  2. Point({24, 0}) → trapStarter
  3. Point({12, 0}) → rectStarter
  4. Polygon((triLength / 3, -2), (triLength / 3 + 1.5, -2), 4) → poly1
  5. Polygon(rectStarter + (rectLength / 3, -2), rectStarter + (rectLength / 3 + 1.5, -2), 4) → poly3
  6. Polygon((-2, triHeight / 3), (-0.5, triHeight / 3), 4) → poly2
  7. Polygon(trapStarter + (trapB1 / 3, -2), trapStarter + (trapB1 / 3 + 1.5, -2), 4) → poly5
  8. Polygon(trapStarter + (trapB2 / 3 + (trapB1 - trapB2) / 2, trapHeight + 0.5), trapStarter + (trapB2 / 3 + (trapB1 - trapB2) / 2 + 1.5, trapHeight + 0.5), 4) → poly6
  9. Polygon(parStarter + (parLength / 3, -2), parStarter + (parLength / 3 + 1.5, -2), 4) → poly8
  10. Polygon(parStarter + (parLength + 3, parHeight / 3), parStarter + (parLength + 4.5, parHeight / 3), 4) → poly9
  11. Polygon(rectStarter + (-2, rectHeight / 3), rectStarter + (-0.5, rectHeight / 3), 4) → poly4
  12. Polygon(trapStarter + (trapB1 / 2 - 2, trapHeight / 3), trapStarter + (trapB1 / 2 - 0.5, trapHeight / 3), 4) → poly7
  13. If(IsInRegion[A, poly9], 1, If[IsInRegion[B, poly9], 2, If[IsInRegion[C, poly9], 3, If[IsInRegion[D, poly9], 4, If[IsInRegion[E, poly9], 5, If[IsInRegion[F, poly9], 6, If[IsInRegion[G, poly9], 7, If[IsInRegion[H, poly9], 8, If[IsInRegion[I, poly9], 9, 0]]]]]]]]) → nineSum
  14. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → eightSum
  15. If(IsInRegion[A, poly6], 1, If[IsInRegion[B, poly6], 2, If[IsInRegion[C, poly6], 3, If[IsInRegion[D, poly6], 4, If[IsInRegion[E, poly6], 5, If[IsInRegion[F, poly6], 6, If[IsInRegion[G, poly6], 7, If[IsInRegion[H, poly6], 8, If[IsInRegion[I, poly6], 9, 0]]]]]]]]) → sixSum
  16. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → fiveSum
  17. If(IsInRegion[A, poly3], 1, If[IsInRegion[B, poly3], 2, If[IsInRegion[C, poly3], 3, If[IsInRegion[D, poly3], 4, If[IsInRegion[E, poly3], 5, If[IsInRegion[F, poly3], 6, If[IsInRegion[G, poly3], 7, If[IsInRegion[H, poly3], 8, If[IsInRegion[I, poly3], 9, 0]]]]]]]]) → threeSum
  18. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → twoSum
  19. Point({0, 0}) → triangleStarter
  20. Polygon(triangleStarter, triangleStarter + (triLength, 0), triangleStarter + (0, triHeight)) → triangle, f, g, h
  21. Polygon(rectStarter, rectStarter + (rectLength, 0), rectStarter + (rectLength, rectHeight), rectStarter + (0, rectHeight)) → rect, i, j, k, p
  22. If(IsInRegion[A, poly1], 1, If[IsInRegion[B, poly1], 2, If[IsInRegion[C, poly1], 3, If[IsInRegion[D, poly1], 4, If[IsInRegion[E, poly1], 5, If[IsInRegion[F, poly1], 6, If[IsInRegion[G, poly1], 7, If[IsInRegion[H, poly1], 8, If[IsInRegion[I, poly1], 9, 0]]]]]]]]) → oneSum
  23. Polygon(trapStarter, trapStarter + (trapB1, 0), trapStarter + ((trapB1 + trapB2) / 2, trapHeight), trapStarter + ((trapB1 - trapB2) / 2, trapHeight)) → trap, q, r, s, t
  24. Segment(trapStarter + (trapB1 / 2, 0), trapStarter + (trapB1 / 2, trapHeight)) → trapHeightSegment
  25. If(IsInRegion[A, poly4], 1, If[IsInRegion[B, poly4], 2, If[IsInRegion[C, poly4], 3, If[IsInRegion[D, poly4], 4, If[IsInRegion[E, poly4], 5, If[IsInRegion[F, poly4], 6, If[IsInRegion[G, poly4], 7, If[IsInRegion[H, poly4], 8, If[IsInRegion[I, poly4], 9, 0]]]]]]]]) → fourSum
  26. If(IsInRegion[A, poly7], 1, If[IsInRegion[B, poly7], 2, If[IsInRegion[C, poly7], 3, If[IsInRegion[D, poly7], 4, If[IsInRegion[E, poly7], 5, If[IsInRegion[F, poly7], 6, If[IsInRegion[G, poly7], 7, If[IsInRegion[H, poly7], 8, If[IsInRegion[I, poly7], 9, 0]]]]]]]]) → sevenSum
  27. Polygon(parStarter, parStarter + (parLength, 0), parStarter + (parLength + 2.5, parHeight), parStarter + (2.5, parHeight)) → par, parstarter, a, b, c
  28. Segment(parStarter + (parLength, 0), parStarter + (parLength + 2.5, 0)) → d
  29. Segment(parStarter + (parLength + 2.5, parHeight), parStarter + (parLength + 2.5, 0)) → e
  30. Sequence(Point[{i, 10}], i, 11, 11 + 24, 3) → anchors

AI Drawing Prompt Reference

Draw a parallelogram, a trapezoid, a rectangle, and a triangle. Start by placing three points on the x-axis to serve as the starting points for each shape. Then, draw each shape, ensuring their sides are parallel or perpendicular to the x-axis. Finally, draw the height or length segments of each shape to observe area changes.
The prompt above was compiled from the original drawing commands and is for reference only.