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What fraction is shaded?

What fraction is shaded?
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2019-03-11 07:34
TriangleProbability & StatisticsGeometric Construction
This example demonstrates the fraction of a shaded area within a triangle. Key mathematical concepts include geometry, triangles, and probability & statistics. Using GeoGebra commands such as Intersect, Point, and Polygon, the shape of the triangle and the shaded area can be dynamically changed to observe the variations in the shaded fraction. Suitable for middle school and above students or teachers for teaching and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → polígono1, f, g, h, i, C, D
  4. Midpoint(i) → E
  5. Midpoint(g) → F
  6. Segment(A, C) → j
  7. Segment(D, B) → k
  8. Segment(C, E) → l
  9. Segment(E, B) → m
  10. Segment(A, F) → n
  11. Segment(F, D) → p
  12. Intersect(j, k) → G
  13. Intersect(l, p) → H
  14. Polygon(D, G, C, H) → c1, d, g_1, c, h_1
  15. Intersect(m, n) → I
  16. Polygon(A, I, B, G) → c2, a, i_1, b, g_2
  17. Vector(E, A) → u
  18. Translate(H, Vector[(Min[Max[0, t], 1] * u)]) → H'
  19. Translate(G, Vector[(Min[Max[0, t], 1] * u)]) → G'
  20. Translate(Translate[D, Vector[(Min[Max[0, t], 1] * u)]], Vector[(Min[Max[0, t - 1], 1] * u)]) → D'
  21. Translate(Translate[C, Vector[(Min[Max[0, t], 1] * u)]], Vector[(Min[Max[0, t - 1], 1] * u)]) → C'
  22. Segment(H', G') → q
  23. Polygon(D', G', C', H') → c3, d', g', c', h'
  24. Polygon(A, I, B) → t1, b_1, a_1, i_2