MathPlotAI Logo MathPlotAI

Area of a Composite Shape

Area of a Composite Shape
Loading the math board and drawing, please wait…
2018-10-08 15:17
PolygonIntegralGeometric Construction
This example demonstrates how to calculate the area of a composite shape using geometric construction. Key mathematical concepts include geometric construction and area calculation. It uses commands like Point, Polygon, and PointIn in GeoGebra. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Point(Circle[W_1, 4]) → Z_1
  2. Polygon(W_1, Z_1, A_2) → t2, a_2, w_1, f
  3. Point(Circle[B_2, 7]) → C_2
  4. Polygon(B_2, C_2, D_2, E_2) → q3, b_2, c_2, d_2, e_2
  5. Point(Circle[F_2, 1]) → G_2
  6. Polygon(F_2, G_2, H_2) → t1, h_2, f_2, g_2
  7. Point(Circle[I_2, 3]) → J_2
  8. Polygon(I_2, J_2, K_2) → t4, k_2, i_2, j_2
  9. Point(Circle[L_2, 3]) → M_2
  10. Polygon(L_2, M_2, N_2, O_2) → q4, l_2, m_2, n_2, o_2
  11. Point(Circle[P_2, 2]) → Q_2
  12. Point(Circle[T_2, 2]) → U_2
  13. Polygon(T_2, U_2, V_2, W_2) → q1, t_2, u_2, v_2, w_2
  14. PointIn(q1) → Pointq1_1
  15. Point(Circle[V_1, 4.47213595499958]) → Z_2
  16. Polygon(V_1, Z_2, L_3, M_3, N_3, A_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3) → poly1, v_1, k_3, l_3, m_3, n_3, z_2, a_3, e_3, f_3, g_3, h_3, i_3, j_3
  17. PointIn(t2) → Pointt2
  18. PointIn(q4) → Pointq4
  19. PointIn(q1) → Pointq1
  20. PointIn(t1) → Pointt1
  21. PointIn(q3) → Pointq3
  22. PointIn(t4) → Pointt4_1
  23. PointIn(t4) → Pointt4

AI Drawing Prompt Reference

Draw a composite shape made of multiple polygons. Start by drawing a circle and taking a point Z1 from it, then use Z1, A2, and W1 to draw a triangle t2. Next, draw a circle with B2 as the center and take a point C2 from it, then use C2, D2, and E2 to draw a quadrilateral q3. Draw another circle with F2 as the center and take a point G2 from it, then use G2 and H2 to draw a triangle t1. Draw a circle with I2 as the center and take a point J2 from it, then use J2 and K2 to draw a triangle t4. Draw a circle with L2 as the center and take a point M2 from it, then use M2, N2, and O2 to draw a quadrilateral q4. Draw a circle with P2 as the center and take a point Q2 from it, then draw a circle with T2 as the center and take a point U2 from it, and use T2, U2, V2, and W2 to draw a quadrilateral q1. Finally, draw a circle with V1 as the center and take a point Z2 from it, and use V1, Z2, L3, M3, N3, A3, E3, F3, G3, H3, I3, J3, and K3 to draw a complex polygon poly1.
The prompt above was compiled from the original drawing commands and is for reference only.