MathPlotAI Logo MathPlotAI

Integer Area

Integer Area
Loading the math board and drawing, please wait…
2019-02-17 19:07
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a geometric shape using integer values. Key mathematical concepts include the calculation of geometric areas. Using GeoGebra commands such as Intersect, Point, Segment, and Polygon, specific geometric shapes are constructed and their areas are calculated.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → Help1
  3. Point(yAxis) → Help2
  4. Segment(A, Help1) → help1
  5. Segment(Help2, A) → help2
  6. Point(help1) → B
  7. Point(help2) → C
  8. Polygon(A, B, D, C) → poly1, a, b, d, c
  9. Text(A3, (xvalue, yvalue - A3)) → B3
  10. Text(A4, (xvalue, yvalue - A4)) → B4
  11. Text(A5, (xvalue, yvalue - A5)) → B5
  12. Text(A6, (xvalue, yvalue - A6)) → B6
  13. Text(A7, (xvalue, yvalue - A7)) → B7
  14. Text(A8, (xvalue, yvalue - A8)) → B8
  15. Text(A9, (xvalue, yvalue - A9)) → B9
  16. Text(A10, (xvalue, yvalue - A10)) → B10
  17. Text(A11, (xvalue, yvalue - A11)) → B11
  18. Text(A2, (xvalue, yvalue - A2)) → B2
  19. Text(A1, (xvalue, yvalue - A1)) → B1
  20. Text(A1, (xvalue + 1 + A1, yvalue + 1)) → C1
  21. Text(A2, (xvalue + 1 + A2, yvalue + 1)) → C2
  22. Text(A3, (xvalue + 1 + A3, yvalue + 1)) → C3
  23. Text(A4, (xvalue + 1 + A4, yvalue + 1)) → C4
  24. Text(A5, (xvalue + 1 + A5, yvalue + 1)) → C5
  25. Text(A6, (xvalue + 1 + A6, yvalue + 1)) → C6
  26. Text(A7, (xvalue + 1 + A7, yvalue + 1)) → C7
  27. Text(A8, (xvalue + 1 + A8, yvalue + 1)) → C8
  28. Text(A9, (xvalue + 1 + A9, yvalue + 1)) → C9
  29. Text(A10, (xvalue + 1 + A10, yvalue + 1)) → C10
  30. Text(A11, (xvalue + 1 + A11, yvalue + 1)) → C11
  31. Text((A1 * 0), (xvalue + 1, yvalue - A1)) → D1
  32. Text((A2 * 0), (xvalue + 1, yvalue - A2)) → D2
  33. Text((A3 * 0), (xvalue + 1, yvalue - A3)) → D3
  34. Text((A4 * 0), (xvalue + 1, yvalue - A4)) → D4
  35. Text((A5 * 0), (xvalue + 1, yvalue - A5)) → D5
  36. Text((A6 * 0), (xvalue + 1, yvalue - A6)) → D6
  37. Text((A7 * 0), (xvalue + 1, yvalue - A7)) → D7
  38. Text((A8 * 0), (xvalue + 1, yvalue - A8)) → D8
  39. Text((A9 * 0), (xvalue + 1, yvalue - A9)) → D9
  40. Text((A10 * 0), (xvalue + 1, yvalue - A10)) → D10
  41. Text((A11 * 0), (xvalue + 1, yvalue - A11)) → D11
  42. Text(A2, (xvalue + 2, yvalue - A2)) → E2
  43. Text(A3, (xvalue + 2, yvalue - A3)) → E3
  44. Text(A4, (xvalue + 2, yvalue - A4)) → E4
  45. Text(A5, (xvalue + 2, yvalue - A5)) → E5
  46. Text(A6, (xvalue + 2, yvalue - A6)) → E6
  47. Text(A7, (xvalue + 2, yvalue - A7)) → E7
  48. Text(A8, (xvalue + 2, yvalue - A8)) → E8
  49. Text(A9, (xvalue + 2, yvalue - A9)) → E9
  50. Text(A10, (xvalue + 2, yvalue - A10)) → E10
  51. Text(A11, (xvalue + 2, yvalue - A11)) → E11
  52. Text(A1, (xvalue + 2, yvalue - A1)) → E1
  53. Text((A2 * 2), (xvalue + 3, yvalue - A2)) → F2
  54. Text((A3 * 2), (xvalue + 3, yvalue - A3)) → F3
  55. Text((A4 * 2), (xvalue + 3, yvalue - A4)) → F4
  56. Text((A5 * 2), (xvalue + 3, yvalue - A5)) → F5
  57. Text((A6 * 2), (xvalue + 3, yvalue - A6)) → F6
  58. Text((A7 * 2), (xvalue + 3, yvalue - A7)) → F7
  59. Text((A8 * 2), (xvalue + 3, yvalue - A8)) → F8
  60. Text((A9 * 2), (xvalue + 3, yvalue - A9)) → F9
  61. Text((A10 * 2), (xvalue + 3, yvalue - A10)) → F10
  62. Text((A11 * 2), (xvalue + 3, yvalue - A11)) → F11
  63. Text((A1 * 2), (xvalue + 3, yvalue - A1)) → F1
  64. Text((A2 * 3), (xvalue + 4, yvalue - A2)) → G2
  65. Text((A3 * 3), (xvalue + 4, yvalue - A3)) → G3
  66. Text((A4 * 3), (xvalue + 4, yvalue - A4)) → G4
  67. Text((A5 * 3), (xvalue + 4, yvalue - A5)) → G5
  68. Text((A6 * 3), (xvalue + 4, yvalue - A6)) → G6
  69. Text((A7 * 3), (xvalue + 4, yvalue - A7)) → G7
  70. Text((A8 * 3), (xvalue + 4, yvalue - A8)) → G8
  71. Text((A9 * 3), (xvalue + 4, yvalue - A9)) → G9
  72. Text((A10 * 3), (xvalue + 4, yvalue - A10)) → G10
  73. Text((A11 * 3), (xvalue + 4, yvalue - A11)) → G11
  74. Text((A1 * 3), (xvalue + 4, yvalue - A1)) → G1
  75. Text((A2 * 4), (xvalue + 5, yvalue - A2)) → H2
  76. Text((A3 * 4), (xvalue + 5, yvalue - A3)) → H3
  77. Text((A4 * 4), (xvalue + 5, yvalue - A4)) → H4
  78. Text((A5 * 4), (xvalue + 5, yvalue - A5)) → H5
  79. Text((A6 * 4), (xvalue + 5, yvalue - A6)) → H6
  80. Text((A7 * 4), (xvalue + 5, yvalue - A7)) → H7
  81. Text((A8 * 4), (xvalue + 5, yvalue - A8)) → H8
  82. Text((A9 * 4), (xvalue + 5, yvalue - A9)) → H9
  83. Text((A10 * 4), (xvalue + 5, yvalue - A10)) → H10
  84. Text((A11 * 4), (xvalue + 5, yvalue - A11)) → H11
  85. Text((A1 * 4), (xvalue + 5, yvalue - A1)) → H1
  86. Text((A1 * 5), (xvalue + 6, yvalue - A1)) → I1
  87. Text((A2 * 5), (xvalue + 6, yvalue - A2)) → I2
  88. Text((A3 * 5), (xvalue + 6, yvalue - A3)) → I3
  89. Text((A4 * 5), (xvalue + 6, yvalue - A4)) → I4
  90. Text((A5 * 5), (xvalue + 6, yvalue - A5)) → I5
  91. Text((A6 * 5), (xvalue + 6, yvalue - A6)) → I6
  92. Text((A7 * 5), (xvalue + 6, yvalue - A7)) → I7
  93. Text((A8 * 5), (xvalue + 6, yvalue - A8)) → I8
  94. Text((A9 * 5), (xvalue + 6, yvalue - A9)) → I9
  95. Text((A10 * 5), (xvalue + 6, yvalue - A10)) → I10
  96. Text((A11 * 5), (xvalue + 6, yvalue - A11)) → I11
  97. Text((A1 * 6), (xvalue + 7, yvalue - A1)) → J1
  98. Text((A2 * 6), (xvalue + 7, yvalue - A2)) → J2
  99. Text((A3 * 6), (xvalue + 7, yvalue - A3)) → J3
  100. Text((A4 * 6), (xvalue + 7, yvalue - A4)) → J4
  101. Text((A5 * 6), (xvalue + 7, yvalue - A5)) → J5
  102. Text((A6 * 6), (xvalue + 7, yvalue - A6)) → J6
  103. Text((A7 * 6), (xvalue + 7, yvalue - A7)) → J7
  104. Text((A8 * 6), (xvalue + 7, yvalue - A8)) → J8
  105. Text((A9 * 6), (xvalue + 7, yvalue - A9)) → J9
  106. Text((A10 * 6), (xvalue + 7, yvalue - A10)) → J10
  107. Text((A11 * 6), (xvalue + 7, yvalue - A11)) → J11
  108. Text((A1 * 7), (xvalue + 8, yvalue - A1)) → K1
  109. Text((A2 * 7), (xvalue + 8, yvalue - A2)) → K2
  110. Text((A3 * 7), (xvalue + 8, yvalue - A3)) → K3
  111. Text((A4 * 7), (xvalue + 8, yvalue - A4)) → K4
  112. Text((A5 * 7), (xvalue + 8, yvalue - A5)) → K5
  113. Text((A6 * 7), (xvalue + 8, yvalue - A6)) → K6
  114. Text((A7 * 7), (xvalue + 8, yvalue - A7)) → K7
  115. Text((A8 * 7), (xvalue + 8, yvalue - A8)) → K8
  116. Text((A9 * 7), (xvalue + 8, yvalue - A9)) → K9
  117. Text((A10 * 7), (xvalue + 8, yvalue - A10)) → K10
  118. Text((A11 * 7), (xvalue + 8, yvalue - A11)) → K11
  119. Text((A1 * 8), (xvalue + 9, yvalue - A1)) → L1
  120. Text((A2 * 8), (xvalue + 9, yvalue - A2)) → L2
  121. Text((A3 * 8), (xvalue + 9, yvalue - A3)) → L3
  122. Text((A4 * 8), (xvalue + 9, yvalue - A4)) → L4
  123. Text((A5 * 8), (xvalue + 9, yvalue - A5)) → L5
  124. Text((A6 * 8), (xvalue + 9, yvalue - A6)) → L6
  125. Text((A7 * 8), (xvalue + 9, yvalue - A7)) → L7
  126. Text((A8 * 8), (xvalue + 9, yvalue - A8)) → L8
  127. Text((A9 * 8), (xvalue + 9, yvalue - A9)) → L9
  128. Text((A10 * 8), (xvalue + 9, yvalue - A10)) → L10
  129. Text((A11 * 8), (xvalue + 9, yvalue - A11)) → L11
  130. Text((A1 * 9), (xvalue + 10, yvalue - A1)) → M1
  131. Text((A2 * 9), (xvalue + 10, yvalue - A2)) → M2
  132. Text((A3 * 9), (xvalue + 10, yvalue - A3)) → M3
  133. Text((A4 * 9), (xvalue + 10, yvalue - A4)) → M4
  134. Text((A5 * 9), (xvalue + 10, yvalue - A5)) → M5
  135. Text((A6 * 9), (xvalue + 10, yvalue - A6)) → M6
  136. Text((A7 * 9), (xvalue + 10, yvalue - A7)) → M7
  137. Text((A8 * 9), (xvalue + 10, yvalue - A8)) → M8
  138. Text((A9 * 9), (xvalue + 10, yvalue - A9)) → M9
  139. Text((A10 * 9), (xvalue + 10, yvalue - A10)) → M10
  140. Text((A11 * 9), (xvalue + 10, yvalue - A11)) → M11
  141. Text((A1 * 10), (xvalue + 11, yvalue - A1)) → N1
  142. Text((A2 * 10), (xvalue + 11, yvalue - A2)) → N2
  143. Text((A3 * 10), (xvalue + 11, yvalue - A3)) → N3
  144. Text((A4 * 10), (xvalue + 11, yvalue - A4)) → N4
  145. Text((A5 * 10), (xvalue + 11, yvalue - A5)) → N5
  146. Text((A6 * 10), (xvalue + 11, yvalue - A6)) → N6
  147. Text((A7 * 10), (xvalue + 11, yvalue - A7)) → N7
  148. Text((A8 * 10), (xvalue + 11, yvalue - A8)) → N8
  149. Text((A9 * 10), (xvalue + 11, yvalue - A9)) → N9
  150. Text((A10 * 10), (xvalue + 11, yvalue - A10)) → N10
  151. Text((A11 * 10), (xvalue + 11, yvalue - A11)) → N11
  152. Polygon((13 + x(B), 0), (13 + x(B) + 1, 0), (13 + x(B) + 1, 12), (13 + x(B), 12)) → poly2, e, f, g, h
  153. Polygon((12, 11 - y(C)), (24, 11 - y(C)), (24, 10 - y(C)), (12, 10 - y(C))) → poly3, i, j, k, l
  154. Segment(E, F) → m
  155. Intersect(h, i) → G
  156. Intersect(h, k) → H
  157. Intersect(f, k) → J
  158. Intersect(f, i) → M
  159. Polygon(H, J, M, G) → poly4, h_1, j_1, m_1, g_1
  160. Polygon(F, N, O, P) → poly5, f_1, n, o, p
  161. Point(f_1) → Q
  162. Polygon(F, Q, R, S) → poly6, f_2, q, r, s
  163. Line((A1, -1), (A1, -2)) → A13
  164. Line((A2, -1), (A2, -2)) → A14
  165. Line((A3, -1), (A3, -2)) → A15
  166. Line((A4, -1), (A4, -2)) → A16
  167. Line((A5, -1), (A5, -2)) → A17
  168. Line((A6, -1), (A6, -2)) → A18
  169. Line((A7, -1), (A7, -2)) → A19
  170. Line((A8, -1), (A8, -2)) → A20
  171. Line((A9, -1), (A9, -2)) → A21
  172. Line((A10, -1), (A10, -2)) → A22
  173. Line((A11, -1), (A11, -2)) → A23
  174. Line((-2, A1), (-1, A1)) → B13
  175. Line((-2, A2), (-1, A2)) → B14
  176. Line((-2, A3), (-1, A3)) → B15
  177. Line((-2, A4), (-1, A4)) → B16
  178. Line((-2, A5), (-1, A5)) → B17
  179. Line((-2, A6), (-1, A6)) → B18
  180. Line((-2, A7), (-1, A7)) → B19
  181. Line((-2, A8), (-1, A8)) → B20
  182. Line((-2, A9), (-1, A9)) → B21
  183. Line((-2, A10), (-1, A10)) → B22
  184. Line((-2, A11), (-1, A11)) → B23
  185. Intersect(A1, a) → T
  186. Intersect(A2, a) → U
  187. Intersect(A3, a) → V
  188. Intersect(A4, a) → W
  189. Intersect(A5, a) → Z
  190. Intersect(A6, a) → A_1
  191. Intersect(A7, a) → B_1
  192. Intersect(A8, a) → C_1
  193. Intersect(A9, a) → D_1
  194. Intersect(A10, a) → E_1
  195. Intersect(A11, a) → F_1
  196. Intersect(A13, a) → C13
  197. Intersect(A14, a) → C14
  198. Intersect(A15, a) → C15
  199. Intersect(A16, a) → C16
  200. Intersect(A17, a) → C17
  201. Intersect(A18, a) → C18
  202. Intersect(A19, a) → C19
  203. Intersect(A20, a) → C20
  204. Intersect(A21, a) → C21
  205. Intersect(A22, a) → C22
  206. Intersect(A23, a) → C23
  207. Intersect(A13, d) → D13
  208. Intersect(A14, d) → D14
  209. Intersect(A15, d) → D15
  210. Intersect(A16, d) → D16
  211. Intersect(A17, d) → D17
  212. Intersect(A18, d) → D18
  213. Intersect(A19, d) → D19
  214. Intersect(A20, d) → D20
  215. Intersect(A21, d) → D21
  216. Intersect(A22, d) → D22
  217. Intersect(A23, d) → D23
  218. Segment(C13, D13) → E13
  219. Segment(C14, D14) → E14
  220. Segment(C15, D15) → E15
  221. Segment(C16, D16) → E16
  222. Segment(C17, D17) → E17
  223. Segment(C18, D18) → E18
  224. Segment(C19, D19) → E19
  225. Segment(C20, D20) → E20
  226. Segment(C21, D21) → E21
  227. Segment(C22, D22) → E22
  228. Segment(C23, D23) → E23
  229. Intersect(B13, c) → F13
  230. Intersect(B14, c) → F14
  231. Intersect(B15, c) → F15
  232. Intersect(B16, c) → F16
  233. Intersect(B17, c) → F17
  234. Intersect(B18, c) → F18
  235. Intersect(B19, c) → F19
  236. Intersect(B20, c) → F20
  237. Intersect(B21, c) → F21
  238. Intersect(B22, c) → F22
  239. Intersect(B23, c) → F23
  240. Intersect(B13, b) → G13
  241. Intersect(B14, b) → G14
  242. Intersect(B15, b) → G15
  243. Intersect(B16, b) → G16
  244. Intersect(B17, b) → G17
  245. Intersect(B18, b) → G18
  246. Intersect(B19, b) → G19
  247. Intersect(B20, b) → G20
  248. Intersect(B21, b) → G21
  249. Intersect(B22, b) → G22
  250. Intersect(B23, b) → G23
  251. Segment(F13, G13) → H13
  252. Segment(F14, G14) → H14
  253. Segment(F15, G15) → H15
  254. Segment(F16, G16) → H16
  255. Segment(F17, G17) → H17
  256. Segment(F18, G18) → H18
  257. Segment(F19, G19) → H19
  258. Segment(F20, G20) → H20
  259. Segment(F21, G21) → H21
  260. Segment(F22, G22) → H22
  261. Segment(F23, G23) → H23
  262. Segment(N, G_1) → t
  263. Segment(G_1, S) → a_1

AI Drawing Prompt Reference

Draw a coordinate system with the origin at the intersection of the x-axis and y-axis. Then, plot four points in the first quadrant to form a rectangle, with point A at the origin, and points B and C on the x-axis, and points C and D on the y-axis. Calculate and label the area of the rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.