平行四边形的面积公式
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本范例通过三个递进式开放问题引导学生探究平行四边形面积公式。①演示问题:给定底边a=6cm和对应高ha=2cm,计算平行四边形面积A=12cm²;②核心概念:利用「底×对应高」公式计算面积,理解不同边长与高度组合为何得到相同结果;③作图要点:使用Polygon绘制平行四边形,用Point和Segment确定顶点与边,用OrthogonalLine作高线,用Intersect求垂足,用Translate演示高平移后形成矩形的过程;④学段用途:适合5-6年级学生理解面积公式原理,培养几何直观与推理能力。
GeoGebra 命令及参数
Textfield(input1) → InputBox1Textfield(input2) → InputBox2Textfield(input3) → InputBox3Textfield(input4) → InputBox4SpeechBubbleRight(E, 10, 2) → Vieleck1Polygon(F, H, G, I) → v1, f, g, h, iSpline({F, Midpoint[F, H], H}, 3) → AnimStreckeSelectedIndex(DD1) → index1SelectedIndex(DD2) → index2SelectedIndex(DD3) → index3Segment(TriAnimP2, TriAnimP3) → jAngle(TriAnimP3, TriAnimP2, TriAnimP1) → αSegment(TriAnimP3, TriAnimP1) → kSegment(TriAnimP2, TriAnimP1) → lSpeechBubbleRight(E, 9, 1.8) → Vieleck2Segment(I, J) → mSegment(J, H) → nTextfield(InputText) → InputBox5Polygon(I, J, F) → v2, p, q, rPolygon(TriAnimP1, TriAnimP2, TriAnimP3) → d1, trianimp3, trianimp1, trianimp2Polygon(I, J, H, G) → v3, i_2, j_1, h_2, g_2SelectedIndex(DD4) → index4SelectedIndex(DD5) → index5Segment(G, H) → Slide2Point(Slide2) → DynP2OrthogonalLine(DynP2, g) → sIntersect(s, Segment[F, I]) → OPoint(Segment[DynP2, Anim2EndP], schieb3) → PPolygon(P, P + Vector[DynP2, O], P + Vector[DynP2, F], P + Vector[DynP2, H]) → v4, p_1, t, a, bPolygon(DynP2, O, I, G) → v5, dynp2, o, i_1, g_1SpeechBubbleRight(POSSpeechStep6, 10, 1.6) → SpeechStep6Angle(P + Vector[DynP2, F], P + Vector[DynP2, O], P) → βText("$\textsf{\textcolor{db6114}{\bold{h_b}}}$", Midpoint[P, P + Vector[DynP2, O]] - (0.5 * UnitOrthogonalVector[Segment[DynP2, O]]), false, true, 0, 0) → Text4SpeechBubbleRight(R, 11.5, 2) → SpeechBubbleStep7Translate(v4, Vector[F, POSVEnd2]) → v4'Translate(DynP2, Vector[F, POSVEnd2]) → DynP2'Translate(O, Vector[F, POSVEnd2]) → O'Translate(I, Vector[F, POSVEnd2]) → I'Translate(G, Vector[F, POSVEnd2]) → G'Polygon(DynP2', O', I', G') → v5', dynp2', o', i', g'Translate(TriAnimP1, Vector[F, POSVEnd1]) → TriAnimP1'Translate(TriAnimP2, Vector[F, POSVEnd1]) → TriAnimP2'Translate(TriAnimP3, Vector[F, POSVEnd1]) → TriAnimP3'Polygon(TriAnimP1', TriAnimP2', TriAnimP3') → d1', trianimp3', trianimp1', trianimp2'Translate(I, Vector[F, POSVEnd1]) → I'_{1}Translate(J, Vector[F, POSVEnd1]) → J'Translate(H, Vector[F, POSVEnd1]) → H'Translate(G, Vector[F, POSVEnd1]) → G'_{1}Polygon(I'_{1}, J', H', G'_{1}) → v3', i'_{1}, j', h', g'_{1}Angle(Translate[P + Vector[DynP2, F], Vector[F, POSVEnd2]], Translate[P + Vector[DynP2, O], Vector[F, POSVEnd2]], Translate[P, Vector[F, POSVEnd2]]) → γAngle(TriAnimP3', TriAnimP2', TriAnimP1') → δPolyLine(G'_{1}, H', J', I'_{1}, G'_{1}) → VEndPoly1PolyLine(TriAnimP3', TriAnimP2', TriAnimP1', TriAnimP3') → VEndPoly2Translate(a, Vector[F, POSVEnd2]) → a'Translate(b, Vector[F, POSVEnd2]) → b'Translate(p_1, Vector[F, POSVEnd2]) → cTranslate(t, Vector[F, POSVEnd2]) → t'Segment(DynP2, P) → dTranslate(F, Vector[F, EndSkizz3POS]) → EndSkizz3P1Translate(H, Vector[F, EndSkizz3POS]) → EndSkizz3P2Translate(G, Vector[F, EndSkizz3POS]) → EndSkizz3P3Translate(I, Vector[F, EndSkizz3POS]) → EndSkizz3P4Midpoint(EndSkizz3P1, EndSkizz3P3) → EndSkizz3MPolyLine({EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P1] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P2] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P3] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P4] * relsizeEndSkizz), EndSkizz3M + (Vector[EndSkizz3M, EndSkizz3P1] * relsizeEndSkizz)}) → EndSkizz3OutlinePoint(EndSkizz3Outline) → TPoint(EndSkizz3Outline) → UPoint(EndSkizz3Outline) → VPoint(EndSkizz3Outline) → WSegment(W, V) → eIntersect(OrthogonalLine[U, e], e) → ZPoint(EndSkizz3Outline) → A_1Intersect(OrthogonalLine[T, Segment[A_1, W]], Segment[A_1, W]) → B_1Segment(B_1, T) → radcon_1Segment(Z, U) → radcon_2Translate(TriAnimP2, Vector[F, POSVEnd1]) → TriAnimP2'_{1}Translate(TriAnimP3, Vector[F, POSVEnd1]) → TriAnimP3'_{1}Segment(TriAnimP2'_{1}, TriAnimP3'_{1}) → j'_{1}Translate(p_1, Vector[F, POSVEnd2]) → f_1
AI 绘图提示语参考
绘制一个平行四边形,给定底边a=6cm和高ha=2cm,计算面积A=12cm²。使用多边形工具绘制平行四边形,通过点和线段定义顶点和边,用垂直线定义高,通过交点确定垂足。将平行四边形通过平移变换为矩形,展示不同边和高的组合可以得到相同的面积。
以上提示语为根据原始绘图命令整理而来,仅供参考。