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Calculating Area of Rhombus by Jordan Varney

Calculating Area of Rhombus by Jordan Varney
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2018-03-05 02:59
PolygonAngleTrigonometryGeometric Construction
This example demonstrates how to calculate the area of a rhombus by constructing its diagonals. Key math concepts include the perpendicularity and bisecting property of diagonals in a rhombus, triangle area formula, and Pythagorean theorem. GeoGebra commands/objects used in construction include Segment, LineBisector, Circle, Intersect, Angle, Polygon, Midpoint, and Rotate. Suitable for high school mathematics education to understand and apply the area calculation method of rhombuses.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. LineBisector(f) → g
  3. Circle(A, B) → c
  4. Intersect(c, g, 2) → C
  5. Intersect(c, g, 1) → D
  6. Intersect(g, f) → E
  7. Segment(C, D) → h
  8. Angle(C, E, A) → α
  9. Polygon(C, E, B) → t1_1, b, c_1, e
  10. Polygon(C, E, A) → t2_1, a, c_2, e_1
  11. Polygon(A, D, E) → t3_1, e_2, a_1, d
  12. Polygon(D, E, B) → t4_1, b_1, d_1, e_3
  13. Midpoint(e_2) → F
  14. Midpoint(e_3) → G
  15. Midpoint(e) → H
  16. Midpoint(e_1) → I
  17. Rotate(C, t1, I) → C'
  18. Rotate(E, t1, I) → E'
  19. Rotate(A, t1, I) → A'
  20. Polygon(C', E', A') → t5, a', c', e'
  21. Rotate(A, t2, F) → A'_1
  22. Rotate(D, t2, F) → D'
  23. Rotate(E, t2, F) → E'_1
  24. Polygon(A'_1, D', E'_1) → t6, e'_1, a'_1, d'
  25. Rotate(D, t3, G) → D'_1
  26. Rotate(E, t3, G) → E'_2
  27. Rotate(B, t3, G) → B'
  28. Polygon(D'_1, E'_2, B') → t7, b', d'_1, e'_2
  29. Rotate(C, t4, H) → C'_1
  30. Rotate(E, t4, H) → E'_3
  31. Rotate(B, t4, H) → B'_1
  32. Polygon(C'_1, E'_3, B'_1) → t8, b'_1, c'_1, e'_3

AI Drawing Prompt Reference

Draw a rhombus and show its diagonals. Start by drawing one side of the rhombus, then find the midpoint of this side and draw its perpendicular bisector. Using the two vertices of the rhombus as centers, draw circles that intersect the bisector at two points, forming the other two vertices of the rhombus. Connect these four points to complete the rhombus and draw its diagonals. Finally, split the rhombus into four congruent triangles using rotations and symmetry to demonstrate the area calculation method of the rhombus.
The prompt above was compiled from the original drawing commands and is for reference only.