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Determining Area vs Perimeter with Block Shapes

Determining Area vs Perimeter with Block Shapes
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2018-10-04 09:51
PolygonInequalityGeometric Construction
This GeoGebra example lets users edit a picture made of blocks to create three different shapes, then find the perimeter and area of each shape, demonstrating that shapes with the same area can have different perimeters and vice versa. Core math concepts include area and perimeter of polygons, their calculation, and the relationship between shape configuration and these measurements. Construction uses the Polygon command to define multiple polygons (poly1, poly2, poly4, poly5, poly6) with vertices at points A, B, C, D, E, F, G, H, L, K, M, N, O, P, Q, R, and segments (f, g, h, i, j, k, l, m, s, t, a, b, c, d, e, f_1, g_1, h_1, i_1) to outline and measure the shapes. Suitable for upper elementary and middle school students, this interactive activity reinforces geometric concepts and encourages exploration of how changing a shape's outline affects its area and perimeter.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(E, D, 4) → poly2, j, k, l, m, F, G
  3. Polygon(K, L, 4, xOyPlane) → poly4, s, t, a, b, M, N
  4. Polygon(G, O, 4) → poly5, c, d, e, f_1, P, Q
  5. Polygon(O, R, 4) → poly6, g_1, h_1, i_1, j_1, S, T
  6. Polygon(E, I, 4) → poly3, n, p, q, r, J, U
  7. Polygon(L, G, 4) → poly7, k_1, l_1, m_1, n_1, V, W
  8. Polygon(O, G, 4) → poly8, p_1, q_1, r_1, s_1, Z, A_1
  9. Polygon(O, R, 4) → poly9, t_1, a_1, b_1, c_1, B_1, C_1
  10. Polygon(P, S, 4) → poly10, d_1, e_1, f_2, g_2, D_1, E_1
  11. Polygon(E, P, 4) → poly11, h_2, i_2, j_2, k_2, F_1, G_1
  12. Polygon(A, D, 4) → poly12, l_2, m_2, n_2, p_2, H_1, I_1
  13. Polygon(C, B, 4) → poly13, q_2, r_2, s_2, t_2, J_1, K_1
  14. Polygon(R, O, 4) → poly14, a_2, b_2, c_2, d_2, L_1, M_1
  15. Polygon(J_1, K, 4, xOyPlane) → poly15, e_2, f_3, g_3, h_3, N_1, O_1
  16. Polygon(A_1, M_1, 4) → poly16, i_3, j_3, k_3, l_3, P_1, Q_1