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Area of Simple Polygons by Splitting (Tangram)

Area of Simple Polygons by Splitting (Tangram)
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2020-05-03 17:09
PolygonTrigonometryGeometric Construction
This example demonstrates calculating the area of simple polygons by splitting tangram shapes. Key math concepts include polygon area calculation, geometric dissection, triangle area formulas, and quadrilateral properties. It uses GeoGebra commands/objects like Point, Polygon, PointIn, and Textfield. Suitable for middle school mathematics teaching to understand polygon area methods and geometric intuition.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 8]) → B
  2. Polygon(A, B, C) → t1, c, a, b
  3. Point(Circle[D, 8]) → E
  4. Polygon(D, E, G) → t2, g, d, e
  5. Point(Circle[F, 4]) → H
  6. Polygon(F, H, I) → t3, i, f, h
  7. Point(Circle[J, 2.8284271247461903]) → K
  8. Polygon(J, K, L, M) → q1, j, k, l, m
  9. Point(Circle[N, 4]) → O
  10. Polygon(N, O, P) → t4, p, n, o
  11. Point(Circle[Q, 4]) → R
  12. Polygon(Q, R, S) → t5, s, q, r
  13. Point(Circle[U, 4]) → V
  14. Polygon(U, V, W, Z) → q2, u, v, w, z_1
  15. PointIn(t2) → Pointt2
  16. PointIn(t1) → Pointt1
  17. PointIn(q1) → Pointq1
  18. PointIn(t3) → Pointt3
  19. PointIn(t4) → Pointt4
  20. PointIn(q2) → Pointq2
  21. PointIn(t5) → Pointt5
  22. Polygon(T, A_1, B_1, C_1, D_1, E_1, F_1) → poly1, t, a_1, b_1, c_1, d_1, e_1, f_1
  23. Polygon(G_1, H_1, I_1, J_1, K_1) → poly2, g_1, h_1, i_1, j_1, k_1
  24. Polygon(L_1, M_1, N_1, O_1, P_1, Q_1) → poly3, l_1, m_1, n_1, o_1, p_1, q_1
  25. Polygon(R_1, S_1, T_1, U_1, V_1, W_1) → poly4, r_1, s_1, t_1, u_1, v_1, w_1
  26. Textfield(SSANS) → InputBox1
  27. Polygon(D_2, E_2, F_2, G_2, H_2) → poly5, d_2, e_2, f_2, g_2, h_2