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Area of a Parallelogram via Dissection into a Rectangle

Area of a Parallelogram via Dissection into a Rectangle
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2014-10-27 02:16
PolygonVectorTransformationGeometric Construction
①This example demonstrates how to derive the area formula of a parallelogram by dissecting it along a height and translating the triangular piece to form a rectangle. ②Core mathematical concepts include the area formula (base × height), geometric transformation (translation), and the principle of area conservation under dissection. ③Construction details: Using GeoGebra commands such as Intersect, Point, Vector, Translate, OrthogonalLine, and Polygon, a parallelogram ABCD is built, and a triangular part is translated to reshape it into a rectangle, with dynamic visualization of the process. ④Suitable for middle school geometry classes or advanced elementary math, helping students understand the origin of the area formula and develop spatial reasoning and transformation thinking.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → C
  3. Vector(A, C) → u
  4. Translate(B, u) → D
  5. OrthogonalLine(B, xAxis) → a
  6. Intersect(a, xAxis) → E
  7. Polygon(A, B, E) → poly1, e, a_1, b
  8. Polygon(A, B, D, C) → poly2, a_2, b_1, d, c
  9. Vector(A, F) → v
  10. Translate(A, v) → A'
  11. Translate(B, v) → B'
  12. Translate(E, v) → E'
  13. Polygon(A', B', E') → poly1', e', a', b'
  14. Polygon(B, E, E', D) → poly3, b_2, e_1, e'_1, d_1

AI Drawing Prompt Reference

Draw a parallelogram, split it into a triangle along a height, and translate the triangle to form a rectangle, demonstrating the derivation of the parallelogram's area formula and emphasizing geometric transformation and area conservation.
The prompt above was compiled from the original drawing commands and is for reference only.