网格中风筝形(Deltoid)面积计算 - 级别1

网格中风筝形(Deltoid)面积计算 - 级别1
几何画板及绘图内容加载中,请稍等……
2023-09-07 13:38
该GeoGebra范例演示如何在网格中计算风筝形(Deltoid,即筝形)的面积,属于基础练习级别。核心数学概念是特殊四边形(平行四边形、梯形、风筝形、菱形)的面积公式应用与推导,重点训练学生将风筝形分解为两个三角形或利用对角线公式求面积。作图要点包括:使用Polygon构造风筝形顶点,通过Segment绘制边和对角线,利用Random和Shuffle生成随机网格位置,用Textfield和Button提供交互输入与验证,并包含validate、showanswer等对象实现即时反馈。适合小学5-6年级学生,用于课堂练习或自主巩固,帮助学生理解面积公式的几何意义并提升计算能力。

GeoGebra 命令及参数

  1. Join(Sequence[Shuffle[{2, 3, 4, 5}], m, 1, 30]) → listEH
  2. Shuffle(Sequence[Random[7, coordheight - 2], m, 1, 100]) → randomNosForX, {10, 7, 9, 8, 8, 9, 8, 7, 9, 9, 7, 7, 9, 7, 9, 7, 9, 9, 8, 8, 10, 10, 8, 10, 10, 9, 8, 10, 7, 10, 7, 9, 8, 8, 7, 7, 7, 7, 9, 10, 7, 7, 8, 9, 8, 7, 10, 8, 7, 10, 10, 7, 10, 10, 9, 8, 9, 9, 10, 9, 9, 10, 10, 8, 7, 7, 9, 7, 7, 9, 10, 10, 9, 10, 7, 8, 10, 9, 10, 9, 9, 7, 10, 9, 7, 7, 9, 9, 9, 10, 8, 9, 10, 9, 9, 9, 9, 7, 8, 8}
  3. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  4. Shuffle(Sequence[Random[4, coordwidth - 2], m, 1, 100]) → randomNosForY, {6, 9, 5, 8, 8, 7, 7, 6, 8, 6, 8, 7, 4, 8, 7, 5, 7, 4, 9, 10, 4, 9, 6, 6, 9, 10, 6, 9, 10, 9, 8, 7, 9, 9, 4, 5, 4, 9, 8, 6, 10, 8, 6, 6, 6, 4, 8, 5, 5, 4, 9, 10, 7, 5, 5, 10, 7, 6, 6, 9, 8, 7, 5, 8, 10, 9, 7, 7, 6, 7, 7, 6, 9, 6, 5, 9, 10, 8, 9, 6, 8, 9, 9, 8, 4, 9, 10, 5, 7, 8, 5, 4, 7, 7, 8, 8, 5, 5, 9, 4}
  5. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  6. Segment(P1, P3) → es
  7. Textfield(input1) → InputBox1
  8. Textfield(input2) → InputBox2
  9. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  10. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  11. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  12. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  13. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  14. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  15. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  16. Flatten(Sequence[Sequence[O + (m * (size, 0)) + (j * (0, size)), m, 0, coordwidth - 1], j, 0, coordheight - 1]) → listPoints
  17. Random(2, numX - 2) → prop
  18. Segment(P4, P2) → fs
  19. Segment(G1, G2) → g
  20. Translate(Segment[(0, -0.1), (0, 0.1)], G1) → h
  21. Translate(Segment[(0, -0.1), (0, 0.1)], G2) → i
  22. Intersect(es, fs) → S
  23. Textfield(input3) → InputBox3
  24. Zip(Polygon[P, P + (0, size), P + (0, size) + (size, 0), P + (size, 0)], P, listPoints) → listCoords
  25. Angle(P2, Midpoint[P2, P4], P1) → α

AI 绘图提示语参考

在坐标网格上先放置一个“菱形/风筝形”的四个顶点,形成两条对角线:一条连接左右上、左右下顶点形成水平方向的对角线,另一条连接上下左右顶点形成竖直方向的对角线。用线段把四个顶点按顺序连成封闭四边形,再标出两条对角线与其交点。随后在对角线上取交点附近的角度位置,从其中一个顶点看向另一个顶点与交点处的射线,画出夹角并放置角度符号。最后可在图上加入输入框用于填写面积相关数值。
以上提示语为根据原始绘图命令整理而来,仅供参考。