Pyramid and Its Net

Loading the math board and drawing, please wait…

2017-03-04 01:41

① This example demonstrates a four-sided pyramid (square pyramid) and its corresponding planar net, showing how a 3D solid unfolds into a 2D shape through linked views. ② Core math concepts include the pyramid's apex, base, lateral edges, triangular faces, and the correspondence between faces and edges in the net, relating to surface area and spatial visualization in solid geometry. ③ Construction details: uses GeoGebra commands Polygon to create the base, Point for vertices, Pyramid to generate the solid, and Net to produce the unfolding; objects include vertices A, B, C, D, E, base poly1, lateral faces faceABE etc., and net faces faceFGHI etc., with edges like edgeAE linking 3D and 2D representations. ④ Suitable for middle/high school geometry lessons, helping students understand pyramid structure, nets, and surface area, and fostering spatial reasoning skills.

GeoGebra Commands & Parameters

Polygon(A, B, C, D) → poly1, a, b, c, d
Point(zAxis) → E
Pyramid(poly1, E) → e, faceABE, faceBCE, faceCDE, faceADE, edgeAE, edgeBE, edgeCE, edgeDE
Net(e, f) → g, F, faceFGJ, faceGHK, faceHIL, faceFIM, edgeFG, edgeGH, edgeHI, edgeFI, edgeFJ, edgeGJ, G, edgeGK, edgeHK, edgeHL, edgeIL, edgeIM, edgeFM, H, I, J, K, L, M, faceFGHI
Net(e, h) → i, N, faceNOR, faceOPS, facePQT, faceNQU, edgeNO, edgeOP, edgePQ, edgeNQ, edgeNR, edgeOR, O, edgeOS, edgePS, edgePT, edgeQT, edgeQU, edgeNU, P, Q, R, S, T, U, faceNOPQ

AI Drawing Prompt Reference

Draw a square pyramid with its net. First, draw a square base ABCD, then place the apex E on the z-axis, construct the pyramid using E and the base ABCD, and finally generate the net of the pyramid, including five lateral faces and four net faces.

The prompt above was compiled from the original drawing commands and is for reference only.