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Exploring Areas of Polygons by Thomas Smith

Exploring Areas of Polygons by Thomas Smith
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2018-10-31 08:38
PolygonTransformationGeometric Construction
This example demonstrates how to explore the areas of polygons using transformations such as rotation and mirroring. Key mathematical concepts include rotation, mirroring, and area calculation of polygons. Using GeoGebra commands like Rotate, Mirror, and Polygon, students can visually understand the methods for calculating polygon areas. Suitable for middle school and above students to learn geometric transformations and area calculations.

GeoGebra Commands & Parameters

  1. Circle(G_1, H_1) → c_1
  2. Tangent(H_1, c_1) → a_1,
  3. Rotate(H_1, (360°) / n, G_1) → I_1
  4. Tangent(I_1, c_1) → b_1,
  5. Intersect(a_1, b_1) → J_1
  6. Mirror(J_1, H_1) → K_1
  7. Polygon(K_1, J_1, n) → poly2, sidelength, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_2, b_2, c_2, e_1, d_2, e_2, f_3, g_3, i_3, j_3, k_3, l_3, m_3, n_3, f_2, p_3, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, g_2, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, h_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, i_2, j_2, k_2, l_2
  8. Segment(G_1, H_1) → radius
  9. PointIn(poly2) → Pointpoly2

AI Drawing Prompt Reference

Draw a circle c_1 with center H_1. Draw two tangents a_1 and b_1 to c_1. Rotate H_1 around I_1 by 360/n degrees to get I_1. Find the intersection J_1 of a_1 and b_1, then reflect J_1 over H_1 to get K_1. Construct an n-sided polygon poly2 using K_1 and J_1 as adjacent vertices. Draw the line segment from G_1 to H_1 as the radius. Randomly select a point inside the polygon as Pointpoly2.
The prompt above was compiled from the original drawing commands and is for reference only.