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Parallelogram Area

Parallelogram Area
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2016-05-09 19:09
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a parallelogram using geometric construction. Key mathematical concepts include the properties of parallelograms and the area formula. Using GeoGebra commands such as Line, Point, Polygon, etc., the construction process is dynamically shown. Suitable for middle school and above students to learn geometry and area calculation.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Point(f) → heightPOINT
  3. OrthogonalLine(heightPOINT, f) → g
  4. Line(B, D) → h
  5. Line(A, h) → i
  6. Line(D, f) → j
  7. Intersect(i, j) → E
  8. Polygon(E, D, B, A) → parallelogram, parallD, parallC, parallB, parallA
  9. Intersect(g, j) → F
  10. Segment(heightPOINT, F) → parallHEIGHT
  11. Angle(parallHEIGHT, parallB) → perpHEIGHT
  12. Vector(B, A) → u
  13. Polygon(B, D, F, heightPOINT) → willSLIDE, willC, willD, willA, willB
  14. Translate(B, u) → B'
  15. Translate(D, u) → D'
  16. Translate(F, u) → F'
  17. Translate(heightPOINT, u) → C'
  18. Polygon(B', D', F', C') → slid, slidC, slidD, slidA, slidB
  19. Polygon(D, F, heightPOINT, B) → HIDEpoly, hideD, hideA, hideB, hideC

AI Drawing Prompt Reference

Draw a parallelogram and demonstrate how to calculate its area. Start by drawing two adjacent sides of the parallelogram, then draw a perpendicular line from one endpoint of one side to the opposite side to find the foot of the perpendicular. Use this foot to measure the height of the parallelogram. Finally, show the area calculation using the base and height, and demonstrate that the area remains unchanged when the parallelogram is slid along one of its sides.
The prompt above was compiled from the original drawing commands and is for reference only.