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Solving for b1 in Trapezoid Area Formula

Solving for b1 in Trapezoid Area Formula
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2015-11-06 22:31
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates using GeoGebra to solve for an unknown in the trapezoid area formula A=1/2(b1+b2)h, focusing on algebraic equation solving within a geometric context. Key math concepts include area calculation, trapezoid properties, and linear equations. GeoGebra commands used in construction are Polygon, Segment, If, PointIn, Point, Vector, and Sequence. Suitable for middle school and high school students learning algebra and geometry applications.

GeoGebra Commands & Parameters

  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