Nets and drawings of three-dimensional figures

Learning Objectives Identify the three-dimensional figure that can be formed from a given net. Draw at least two different valid nets for a given cube, rectangular prism, and triangular prism. Create isometric drawings of simple three-dimensional figures on dot paper. Create orthographic projections (top, front, and side views) of a three-dimensional figure. Interpret a set of orthographic projections to sketch the corresponding three-dimensional figure. Relate the surface area of a 3D figure to the total area of its net. How does a flat piece of cardboard become a shipping box? 📦 This lesson explores how we can represent 3D objects in a 2D world! We will learn how to 'unfold' three-dimensional figures into two-dimensional patterns called nets, and how to draw th...

TermDefinitionExample Three-Dimensional Figure (Solid)A geometric figure that has three dimensions: length, width, and height. It occupies space.A cube, a sphere, a pyramid, or a cylinder. NetA two-dimensional pattern that can be folded along its edges to form a three-dimensional figure. It is like the 'unfolded' version of a solid.A cross shape made of six squares is a net for a cube. Isometric DrawingA method for visually representing three-dimensional objects in two dimensions, where the object is viewed from an angle to reveal multiple sides. All vertical lines are drawn vertically, and all horizontal lines are drawn at a 30° angle to the horizontal.A drawing of a cube on isometric dot paper where all faces are visible and edges appear to be of equal length. Orthographic Pro...

Euler's Formula for Polyhedra V - E + F = 2 For any convex polyhedron, the number of Vertices (V) minus the number of Edges (E) plus the number of Faces (F) will always equal 2. Use this formula to check if you have correctly counted the parts of a solid or to find a missing value. Surface Area from a Net SA = \sum_{i=1}^{n} A_i The total Surface Area (SA) of a 3D figure is the sum of the areas of all the individual shapes (faces) in its net. To find the surface area, calculate the area of each 2D shape in the net and add them all together.