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Calculate the Area of Special Quadrilaterals

Calculate the Area of Special Quadrilaterals
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2023-12-05 23:34
PolygonCoordinate GeometryGeometric Construction
In collections Trapez - Flächeninhalt
This example demonstrates how to calculate the areas of special quadrilaterals (parallelogram, trapezoid, rhombus, square) using GeoGebra. The construction summary includes commands like Join, Sequence, Zip, etc., to clearly show the construction points. Suitable for 5-6 grade students for practice.

GeoGebra Commands & Parameters

  1. Join(Sequence[Shuffle[Sequence[1, maxexnum]], m, 1, 15]) → randomNos
  2. Sequence(m, m, 5, 9) → listPool
  3. Sequence(RandomElement[listPool], m, 1, 110) → randomNosForA, {8, 6, 9, 9, 8, 8, 7, 7, 5, 9, 8, 9, 5, 9, 9, 6, 7, 5, 5, 5, 6, 9, 5, 9, 7, 9, 8, 8, 9, 7, 8, 6, 7, 7, 9, 8, 6, 6, 8, 5, 5, 9, 7, 9, 8, 6, 6, 6, 9, 5, 9, 5, 8, 7, 7, 9, 5, 8, 7, 6, 6, 7, 7, 8, 6, 7, 6, 7, 8, 7, 6, 6, 7, 5, 5, 9, 7, 5, 7, 9, 6, 8, 7, 8, 6, 6, 5, 9, 7, 7, 8, 5, 5, 5, 7, 8, 6, 8, 7, 6, 6, 7, 8, 6, 9, 5, 6, 6, 5, 6}
  4. Sequence(Random[4, 7], m, 1, 110) → randomNosForH, {6, 5, 7, 5, 6, 5, 4, 7, 6, 5, 5, 5, 4, 4, 7, 7, 7, 4, 7, 4, 6, 5, 7, 7, 5, 4, 7, 5, 4, 5, 7, 4, 5, 7, 6, 7, 7, 6, 7, 7, 6, 6, 5, 5, 6, 7, 7, 6, 5, 5, 6, 5, 4, 6, 6, 4, 5, 5, 6, 7, 6, 7, 5, 7, 5, 6, 6, 6, 6, 4, 5, 4, 6, 5, 4, 5, 4, 7, 4, 6, 6, 5, 4, 6, 6, 5, 7, 5, 7, 4, 5, 7, 5, 7, 7, 6, 6, 6, 5, 7, 5, 6, 4, 7, 4, 5, 7, 6, 6, 4}
  5. Sequence((Random[5, 20] * 0.1), m, 1, 110) → randomNosForAbsLinks, {1.1, 0.7000000000000001, 0.6000000000000001, 0.7000000000000001, 2, 1.2000000000000002, 1.9000000000000001, 1.5, 1.1, 0.6000000000000001, 1.7000000000000002, 1.6, 1.5, 1.7000000000000002, 1, 0.5, 0.6000000000000001, 1.9000000000000001, 0.7000000000000001, 1.8, 0.6000000000000001, 2, 1.6, 1.4000000000000001, 2, 1.5, 1.3, 0.7000000000000001, 1.3, 1.2000000000000002, 1.9000000000000001, 0.9, 1, 0.7000000000000001, 1.7000000000000002, 1.5, 1.7000000000000002, 1.6, 0.5, 1.5, 1.3, 1.3, 0.9, 1.1, 1, 1.1, 1.8, 1.4000000000000001, 1.1, 1.6, 1.5, 1.2000000000000002, 0.9, 0.5, 1.4000000000000001, 1.3, 1.1, 1.4000000000000001, 1.1, 1.1, 0.8, 0.5, 1.4000000000000001, 1.6, 1.8, 1.7000000000000002, 1.1, 1.6, 1.4000000000000001, 1.8, 0.8, 1, 0.8, 0.7000000000000001, 1.6, 1.5, 1.2000000000000002, 0.9, 1.8, 1.2000000000000002, 1.8, 1.2000000000000002, 1.3, 0.9, 1.6, 2, 1.1, 1.7000000000000002, 0.6000000000000001, 1.4000000000000001, 1.2000000000000002, 1.8, 1.2000000000000002, 2, 1.6, 0.8, 1.2000000000000002, 0.6000000000000001, 1.8, 0.5, 0.8, 1.2000000000000002, 2, 1.5, 1.9000000000000001, 0.7000000000000001, 0.7000000000000001, 0.8, 1.1, 0.5}
  6. Zip(Random[3, m - 1], m, randomNosForA) → randomNosForC
  7. Sequence(RandomElement[Sequence[0.3, 0.5, 0.01]], m, 1, 110) → randomNosForProp, {0.4200000000000001, 0.5000000000000001, 0.4300000000000001, 0.49000000000000016, 0.31, 0.5000000000000001, 0.4300000000000001, 0.4300000000000001, 0.4100000000000001, 0.49000000000000016, 0.5000000000000001, 0.35000000000000003, 0.34, 0.38000000000000006, 0.33, 0.4300000000000001, 0.4300000000000001, 0.4500000000000001, 0.35000000000000003, 0.4400000000000001, 0.32, 0.39000000000000007, 0.36000000000000004, 0.39000000000000007, 0.35000000000000003, 0.4100000000000001, 0.34, 0.4300000000000001, 0.49000000000000016, 0.4100000000000001, 0.32, 0.37000000000000005, 0.32, 0.33, 0.4200000000000001, 0.4300000000000001, 0.33, 0.34, 0.37000000000000005, 0.36000000000000004, 0.4200000000000001, 0.4400000000000001, 0.38000000000000006, 0.5000000000000001, 0.36000000000000004, 0.48000000000000015, 0.4400000000000001, 0.48000000000000015, 0.4400000000000001, 0.5000000000000001, 0.39000000000000007, 0.33, 0.37000000000000005, 0.34, 0.35000000000000003, 0.4100000000000001, 0.48000000000000015, 0.4100000000000001, 0.48000000000000015, 0.46000000000000013, 0.35000000000000003, 0.4100000000000001, 0.4500000000000001, 0.4400000000000001, 0.3, 0.5000000000000001, 0.4000000000000001, 0.37000000000000005, 0.3, 0.49000000000000016, 0.4500000000000001, 0.32, 0.35000000000000003, 0.31, 0.4000000000000001, 0.39000000000000007, 0.48000000000000015, 0.31, 0.39000000000000007, 0.32, 0.38000000000000006, 0.31, 0.31, 0.4300000000000001, 0.5000000000000001, 0.47000000000000014, 0.49000000000000016, 0.37000000000000005, 0.4300000000000001, 0.4200000000000001, 0.4400000000000001, 0.4500000000000001, 0.46000000000000013, 0.47000000000000014, 0.4400000000000001, 0.34, 0.31, 0.4300000000000001, 0.4500000000000001, 0.32, 0.33, 0.48000000000000015, 0.36000000000000004, 0.34, 0.4200000000000001, 0.49000000000000016, 0.4200000000000001, 0.31, 0.33, 0.38000000000000006}
  8. Textfield(input1) → InputBox1
  9. Textfield(input2) → InputBox2
  10. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  11. Append(true, Sequence[If[randomNosForA(i) ≟ randomNosForA(i - 1), false, true], i, 2, 100]) → stayX
  12. Append(true, Sequence[If[randomNosForC(i) ≟ randomNosForC(i - 1), false, true], i, 2, 100]) → stayY
  13. Remove(Sequence[If[stayX(i), randomNosForA(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  14. Remove(Sequence[If[stayY(i), randomNosForC(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  15. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  16. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  17. Defined(input1) → fixed
  18. NumberSeparationComma((numA * numC)) → numberSeparationZaehler
  19. Intersect(Line[D, yAxis], Line[A, B]) → S
  20. Angle(B, S, D) → α
  21. Segment(D, S) → f
  22. Segment(A, B) → streckea
  23. Segment(C, D) → streckec
  24. If((10 * numD) - floor((10 * numD)) < 0.5, (floor((10 * numD)) * 0.1), (floor((10 * numD)) * 0.1) + 0.1) → numDround
  25. If((10 * numB) - floor((10 * numB)) < 0.5, (floor((10 * numB)) * 0.1), (floor((10 * numB)) * 0.1) + 0.1) → numBround
  26. Segment(B, C) → streckeb
  27. Segment(A, D) → strecked

AI Drawing Prompt Reference

On a coordinate plane, draw a construction diagram for special quadrilaterals: place four corners in a specific order (top-left, top-right, bottom-right, bottom-left) and connect them to form a closed polygon. Identify a key intersection point by intersecting two lines defined by the construction. From this intersection point, draw the segment to a chosen endpoint and also create the angle at the middle vertex using that intersection point and the two rays through the relevant endpoints. Finally, draw the additional segments between the corresponding vertices so the figure clearly shows the relationships among vertices, the intersection point, the drawn sides, and the constructed angle.
The prompt above was compiled from the original drawing commands and is for reference only.