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Square Tiles Around a Rectangular Pool: Writing Algebraic Expressions

Square Tiles Around a Rectangular Pool: Writing Algebraic Expressions
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2012-06-25 13:03
PolygonSequenceCoordinate GeometryGeometric Construction
In collections CBSE Class VI Maths Expressions and equations Expressions and equations Expressions and equations Expressions and equations
This GeoGebra example demonstrates square tiles placed around a blue rectangular pool and guides users to derive an algebraic expression for the total number of tiles required. Core mathematical concepts include algebraic modeling, the relationship between rectangular dimensions and perimeter-based counting, discrete-to-continuous geometric reasoning, and the use of variables to represent length and width. Construction highlights, drawn from the command summary, involve the Polygon command to create the pool polygon PoolPolygon and tile regions, the Sequence command to generate horizontal lines horizontallines and vertical lines verticallines, and the Midpoint command to locate key points; objects such as vertices A, B, C, D, parameters width and length, and auxiliary polygons Method1PolyA, Method1PolyB, Method1PolyC are used to structure the visualization. The resource is suitable for middle school algebra-geometry integration lessons and high school modeling introductions, helping teachers and students abstract a general formula from a concrete tiling pattern.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → PoolPolygon, a_1, b_1, c, d
  2. Sequence(Segment[(x(E), y(E) + a * i), (x(E) + (length + 2.0) * a, y(E) + a * i)], i, 0.0, width + 2.0) → horizontallines
  3. Sequence(Segment[(x(E) + a * i, y(E)), (x(E) + a * i, y(E) + (width + 2.0) * a)], i, 0.0, length + 2.0) → verticallines
  4. Polygon(E, I, A, P) → Method1PolyA, e, i, a_2, p
  5. Polygon(I, J, B, A) → Method1PolyB, i_1, j, b, a_3
  6. Polygon(J, F, K, B) → Method1PolyC, j_1, f, k, b_2
  7. Polygon(B, K, L, C) → Method1PolyD, b_3, k_1, l, c_1
  8. Polygon(C, L, G, M) → Method1PolyE, c_2, l_1, g, m
  9. Polygon(D, C, M, N) → Method1PolyF, d_1, c_3, m_1, n
  10. Polygon(O, D, N, H) → Method1PolyG, o, d_2, n_1, h
  11. Polygon(P, A, D, O) → Method1PolyH, p_1, a_4, d_3, o_1
  12. Polygon(E, F, K, P) → Method2PolyA, e_1, f_1, k_2, p_2
  13. Polygon(O, L, G, H) → Method2PolyB, o_2, l_2, g_1, h_1
  14. Polygon(P, A, D, O) → Method2PolyC, p_3, a_5, d_4, o_3
  15. Polygon(B, K, L, C) → Method2PolyD, b_4, k_3, l_3, c_4
  16. Polygon(E, J, B, P) → Method3PolyA, e_2, j_2, b_5, p_4
  17. Polygon(J, F, L, C) → Method3PolyB, j_3, f_2, l_4, c_5
  18. Polygon(D, L, G, N) → Method3PolyC, d_5, l_5, g_2, n_2
  19. Polygon(P, A, N, H) → Method3PolyD, p_5, a_6, n_3, h_2
  20. Polygon(O, L, G, H) → Method4PolyA, o_4, l_6, g_3, h_3
  21. Polygon(E, I, D, O) → Method4PolyB, e_3, i_2, d_6, o_5
  22. Polygon(J, F, L, C) → Method4PolyC, j_4, f_3, l_7, c_6
  23. Polygon(I, J, B, A) → Method4PolyD, i_3, j_5, b_6, a_7
  24. Polygon(U, V, W, Z) → poly1, u, v, w, z
  25. Polygon(V, A_1, B_1, W) → poly2, v_1, a_8, b_7, w_1
  26. Midpoint(a_1) → C_1
  27. Midpoint(d) → D_1

AI Drawing Prompt Reference

Draw a blue rectangular pool and surround it with square tiles. First, draw the pool's rectangular boundary, then generate tile areas using horizontal and vertical lines. Next, create auxiliary polygons to determine the tile layout, and finally use the midpoint command to find key points.
The prompt above was compiled from the original drawing commands and is for reference only.