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解梯形面积公式求底边b1

解梯形面积公式求底边b1
几何画板及绘图内容加载中，请稍等……
2015-11-06 22:31
函数三角函数解析几何几何作图
①本范例演示如何通过 GeoGebra 解析几何工具，求解梯形面积公式 A=1/2(b1+b2)h 中的未知数 b1；②涉及的核心数学概念包括代数方程求解、梯形面积公式、线性方程；③作图要点提炼自 GeoGebra 命令：Polygon（多边形）、Segment（线段）、If（条件判断）、PointIn（点在线上判断）、Point（点）、Vector（向量）、Sequence（序列）；④适合初中及以上数学学习者，用于理解代数方程在几何图形中的应用和解法。

GeoGebra 命令及参数

  1. Polygon((0, -1.5), (5, -1.5), (5, 3), (0, 3)) → row4Step3, i, j, k, l
  2. Polygon((0, 0), (12, 0), (12, 6), (0, 6)) → row2Step1, e, f, g, b_3
  3. Polygon((0, 3), (5, 3), (5, 5), (0, 5)) → row3step2, m, n, p, q
  4. Polygon((5, -1.5), (12, -1.5), (12, 0), (5, 0)) → row2Check, r, s, checkBottomDivider, a_1
  5. Polygon((0, 6), (12, 6), (12, 7), (0, 7)) → row1Header, a_2, b, c, d
  6. Segment((x(Corner[solve2a_1, 1]), 2.1), (x(Corner[solve1_2, 2]), 2.1)) → step2segment
  7. If(b_4 - h ≟ 0 ∧ (a ≠ (-constR)) ∨ solution ≟ Infinity, true, false) → notValid
  8. Segment((5, 5), (5, 7)) → segmentDivider
  9. Segment((x(Corner[solve2a_1, 1]), 0), (x(Corner[solve1_2, 2]), 0)) → step3segment
  10. PointIn(Polygon[(5.5, 2), (10, 2), (10, 4), (5.5, 4)]) → E
  11. PointIn(Polygon[(5.5, 0.5), (10, 0.5), (10, 1.5), (5.5, 1.5)]) → B
  12. Point(Segment[B + (0.5, 0), (11, y(B))]) → C
  13. Point(Segment[E + (0.5, 0), (11, y(E))]) → D
  14. Segment(Midpoint[B, C], (x(Midpoint[B, C]), y(D))) → height
  15. Polygon(B, C, D, E) → trap, b_1, trapR, b_2, trapL
  16. Vector((If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, (y(D) - y(C)) / 2 + 0.1), (If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, 0)) → heightVectorBottom
  17. Vector((If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, (y(D) - y(C)) / 2 - 0.1), (If[x(C) > x(D), x(C), x(D)], y(D)) + (0.25, 0)) → heightVectorTop
  18. Segment((5, 5), (12, 5)) → checkTopDivider
  19. Sequence(Segment[(5.5 + i, 0), (5.5 + i, 5)], i, 0, 6, 0.5) → gridV
  20. Sequence(Segment[(5, 0.5 + i), (12, 0.5 + i)], i, 0, 4, 0.5) → gridH