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飞机尾翼的面积计算

飞机尾翼的面积计算
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2015-11-12 23:11
测试改名0解析几何几何作图
所属专题 CCSS Support Math I Unit 6
本范例演示了一个玩具飞机尾翼的形状是一个钝角三角形，通过计算钝角三角形的面积来了解三角形面积的计算方法。涉及的核心数学概念包括三角形面积公式。构造摘要中使用了Circle（圆）、Point（点）、Segment（线段）、Intersect（交点）等GeoGebra命令。适合初中及以上学生学习三角形面积计算。

GeoGebra 命令及参数

  1. LaTeX("\text{Identify the measurements that are needed to find the area.}") → text1_2
  2. LaTeX("\text{base and the height are needed.}") → text1_4
  3. LaTeX("\text{Find the area of the fin.}") → text1_7
  4. LaTeX("\text{ \textcolor{#000099}{A=\frac{1}{2}bh}}") → text1_9
  5. LaTeX("\text{The formula for finding the area of a triangle is \textcolor{#000099}{Area =\frac{1}{2}base\; •\; height }}") → text1_8
  6. LaTeX("\text{Area formula for a triangle}") → text1_{11}
  7. LaTeX("\text{Simplify.}") → text1_{15}
  8. LaTeX("\text{of \textcolor{#000099}{2} after the unit.}") → text1_{17}
  9. Circle(A, a) → c
  10. Point(c) → B
  11. Segment(A, B) → b_1
  12. Circle(A, b) → d
  13. OrthogonalLine(C, b_1) → e
  14. Intersect(d, e, 2) → D
  15. Segment(A, D) → f
  16. Segment(D, B) → h
  17. Segment(D, C) → i
  18. FitLineY({C, A}) → g
  19. Segment(C, A) → j
  20. Intersect(g, i) → E
  21. Intersect(g, b_1) → F
  22. Intersect(g, b_1) → G
  23. Segment(H, I) → k
  24. Point(j) → J
  25. Segment(I, J) → l
  26. Segment(H, C) → m
  27. Segment(J, C) → n
  28. Point(b_1) → K
  29. OrthogonalLine(K, b_1) → p
  30. Intersect(b_1, p) → O
  31. Point(b_1) → L
  32. FitLineY({L, M}) → q
  33. OrthogonalLine(M, q) → s
  34. Intersect(p, s) → N
  35. Segment(K, N) → r
  36. Segment(L, M) → t
  37. Segment(K, N) → a_1
  38. Segment(M, N) → c_1
  39. LaTeX((((("\text{ \textcolor{#000099}{A=\frac{1}{2}(" * a1) * ")(") * b1) * ")}}")) → text1_{12}
  40. LaTeX((("\text{ \textcolor{#000099}{A=" * sol) * "}}")) → text1_{13}
  41. LaTeX((("\text{The area of the toy airplane’s fin is \textcolor{#000099}{" * sol) * "} square centimeters.}")) → text1_{18}
  42. LaTeX((((("\text{Substitute \textcolor{#000099}{" * a1) * "} for \textcolor{#000099}{b} and \textcolor{#000099}{") * b1) * "} for \textcolor{#000099}{h}.}")) → text1_{14}
  43. LaTeX("\text{\mathbf{Area} the amount of space inside the boundary of a two-dimensional figure.}") → text5
  44. LaTeX("\text{\mathbf{Obtuse \;angle} an angle measuring greater than 90° but less than 180°.}") → text5_1
  45. LaTeX((((("\text{or \textcolor{#000099}{ A=\frac{1}{2}bh}.Substitute \textcolor{#000099}{" * a1) * "} for the base and \textcolor{#000099}{") * b1) * "} for the height.}")) → text1_{10}
  46. LaTeX((("\text{vertical dashed line of the right triangle,is \textcolor{#000099}{" * b1) * "} centimeters.}")) → text1_6
  47. LaTeX("\text{Recall that area is given in square units,indicated by an exponent}") → text1_{16}
  48. LaTeX("\text{The fin is a triangle.To find the area of a triangle,the length of the}") → text1_3
  49. LaTeX((("\text{The base of the fin is \textcolor{#000099}{" * a1) * "} centimeters and the height,as noted by the}")) → text1_5
  50. LaTeX("\text{}") → text1_1
  51. LaTeX("\text{The fin on a toy airplane is in the shape of an obtuse triangle, as shown in the diagram. What is the area of the fin?}") → text1