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Area of a House Open Middle Problem

Area of a House Open Middle Problem
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2020-12-23 21:59
Coordinate GeometryOptimizationGeometric Construction
This example demonstrates how to construct a house layout on GeoGebra and calculate its area. It involves core math concepts like area, geometry, perimeter, rectangles, triangles, median lines, squares, 3D vectors, linear programming or optimization, and arithmetic operations. The construction uses GeoGebra commands/objects such as Intersect, Segment, Point, Polygon, Midpoint, Dilate, Rotate, and Angle. It is suitable for high school students learning geometric constructions and optimization problems.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(A, C) → f
  3. Segment(C, E) → g
  4. Segment(F, D) → h
  5. Point(h) → G
  6. Segment(F, G) → i
  7. Segment(B, E) → j
  8. Segment(A, B) → k
  9. Segment(C, G) → l
  10. Segment(E, G) → m
  11. Polygon(A, B, E, C) → q1, a_1, b_1, e, c
  12. Polygon(C, F, G) → t1, g_1, c_1, f_1
  13. Polygon(F, E, G) → t2, g_2, f_2, e_1
  14. Midpoint(l) → I
  15. Midpoint(m) → J
  16. Dilate(C, If[0 < d ≤ 1, 1 - d, 0], E) → C'
  17. Polygon(G, C', F) → t3, f_3, g_3, c'
  18. Rotate(G, If[1 < d ≤ 2, ((d - 1) * π), π], J) → G'
  19. Rotate(C', If[1 < d ≤ 2, ((d - 1) * π), π], J) → C''
  20. Rotate(F, If[1 < d ≤ 2, ((d - 1) * π), π], J) → F'
  21. Polygon(G', C'', F') → t3', f', g', c''
  22. Segment(G, C') → n
  23. Segment(G', F') → p
  24. Segment(F', C'') → q
  25. Segment(C'', G') → r
  26. Angle(G, F, C) → α

AI Drawing Prompt Reference

Draw a house layout on a coordinate plane. Start with the axes and mark their intersection. Connect several key points to form the main outline, which consists of two rectangular regions, one of which is divided by a diagonal into two triangles. Place a movable point on one side and draw segments from it to adjacent vertices, then mark the midpoints of two of these segments. Based on a variable parameter, apply scaling or rotation to one of the triangles to create an adjustable additional region. Finally, label an angle to show the geometric relationship. The final figure includes straight lines, polygons, midpoints, transformed polygons, and an angle marker.
The prompt above was compiled from the original drawing commands and is for reference only.