梯形面积变化的影响
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本范例演示梯形面积在平行边长度和高度变化时的变化规律。核心数学概念包括梯形面积公式及其应用。通过GeoGebra命令如Polygon、Segment、Angle等进行几何作图。适合初中5-6年级学生学习和练习梯形面积计算与证明。
GeoGebra 命令及参数
Textfield(input1) → InputBox1Textfield(input2) → InputBox2SelectedIndex(dropDownH) → index2SelectedIndex(dropDownAC) → index1Sequence(Sequence[(IGotOptions(i) * IGotOptions(k)), i, 1, 4], k, 1, 4) → SolMatrix, {{0.25, 1, 0.125, 0.5}, {1, 4, 0.5, 2}, {0.125, 0.5, 0.0625, 0.25}, {0.5, 2, 0.25, 1}}Element(SolMatrix, matrixAC, matrixH) → matrixsolIf(matrixsol ≟ 1 / 16, 2, matrixsol ≟ 2, 7, matrixsol ≟ 4, 8, matrixsol ≟ 1 / 8, 3, matrixsol ≟ 1 / 4, 4, matrixsol ≟ 1 / 2, 5, matrixsol ≟ 1, 6) → solindexPolygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 7, 0, 6, 7, 6, 5, 9, 5, 1, 2, 6, 9, 8, 0, 2, 9, 1, 6, 6, 5, 1, 3, 10, 10, 1, 0, 5, 3, 3, 7, 3, 1, 3, 5, 5, 0, 7, 0, 4, 9, 0, 5, 1, 7, 5, 4, 10, 0, 6, 8, 0, 3, 0, 1, 6, 4, 2, 3, 9, 0, 8, 10, 10, 5, 4, 1, 2, 3, 5, 7, 9, 0, 9, 8, 6, 9, 1, 4, 10, 1, 0, 6, 3, 6, 8, 3, 8, 10, 2, 9, 9, 7, 8, 7, 1, 0, 5, 0, 1}Element(randomNosForX, Mod[questionCount, 100] + 1) → numXShuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 9, 5, 2, 3, 9, 5, 7, 1, 1, 3, 4, 9, 5, 4, 3, 7, 3, 0, 6, 9, 2, 1, 7, 10, 3, 3, 3, 0, 0, 0, 1, 6, 8, 10, 1, 1, 7, 0, 7, 0, 2, 5, 9, 5, 5, 6, 7, 4, 0, 10, 2, 6, 10, 3, 10, 0, 10, 9, 0, 7, 3, 8, 3, 0, 1, 0, 1, 5, 1, 7, 2, 2, 10, 1, 4, 10, 6, 4, 10, 3, 6, 8, 6, 6, 7, 9, 0, 3, 4, 3, 5, 3, 9, 3, 5, 4, 1, 0, 8}Element(randomNosForY, Mod[questionCount, 100] + 1) → numYAppend(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayXAppend(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayYRemove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeatRemove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeatElement(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeatElement(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeatSelectedIndex(dropDownResult) → index4Polygon(A, B, C, D) → q1, a, b, c, dOrthogonalLine(C, a) → gIntersect(g, a) → ESegment(C, E) → hIf(SelectedElement[dropDownH] ≟ dropDownH(1), lenH, SelectedElement[dropDownH] ≟ dropDownH(2), lenH / 2, SelectedElement[dropDownH] ≟ dropDownH(3), (lenH * 2), SelectedElement[dropDownH] ≟ dropDownH(4), lenH / 4, index2 ≟ 5, lenH) → lenHAdaptedIf(SelectedElement[dropDownAC] ≟ dropDownH(1), lenA, index1 ≟ 5, lenA, SelectedElement[dropDownAC] ≟ dropDownH(2), lenA / 2, SelectedElement[dropDownAC] ≟ dropDownH(3), (lenA * 2), SelectedElement[dropDownAC] ≟ dropDownH(4), lenA / 4, SelectedElement[dropDownAC] ≟ dropDownH(5), (lenA * 4)) → lenAAdaptedIf(SelectedElement[dropDownAC] ≟ dropDownH(1), lenC, index1 ≟ 5, lenC, SelectedElement[dropDownAC] ≟ dropDownH(2), lenC / 2, SelectedElement[dropDownAC] ≟ dropDownH(3), (lenC * 2), SelectedElement[dropDownAC] ≟ dropDownH(4), lenC / 4, SelectedElement[dropDownAC] ≟ dropDownH(5), (lenC * 4)) → lenCAdaptedPolygon(A1, B1, C1, D1) → q2, a1, b1, c1, d1OrthogonalLine(C1, a1) → iIntersect(i, a1) → FSegment(C1, F) → h_1PolyLine(A, D, C, B) → Trapez1ZugSegment(A, D) → jSegment(CoordSystem2, CoordSystem3) → kSegment(CoordSystem2, CoordSystem1) → lSequence(CoordSystem2 + ((i * 0.5), 0), i, 0, 28) → l1Sequence(Segment[l1(i), l1(i) + (0, 4.5)], i, 1, Length[l1]) → l2Sequence(CoordSystem2 + (0, (i * 0.5)), i, 0, 9) → l3Sequence(Segment[l3(i), l3(i) + (14, 0)], i, 1, Length[l3]) → l4Angle(C, E, A) → αAngle(C1, F, A1) → βSelectedIndex(DD) → index3Text("\textsf{||}", Midpoint[D, C] + (0, 0.05), false, true, 0, 0) → Text7Text("\textsf{||}", Midpoint[A, B] + (0, 0.05), false, true, 0, 0) → Text8Text("\textsf{||}", Midpoint[D1, C1] + (0, 0.05), false, true, 0, 0) → Text5Text("\textsf{||}", Midpoint[B1, A1] + (0, 0.05), false, true, 0, 0) → Text6Text(Text12, G, false, true, 0, 0) → Text14Text(Text13, H, false, true, 0, 0) → Text15Text(Text3, I, false, true, -1, 0) → Text17Text(Text4, J, false, true, 1, 0) → Text18
AI 绘图提示语参考
画一个梯形,展示其面积随平行边长度和高度变化的情况。梯形的两条平行边和高度可以调整,用不同颜色和标签标示出平行边和高度。在梯形下方绘制一个坐标系,并在坐标系中用不同颜色标示出梯形面积随平行边长度和高度变化的函数图像。在梯形旁边标注出平行边长度和高度的数值,并在坐标系中标注出函数图像的数值。
以上提示语为根据原始绘图命令整理而来,仅供参考。