Nets of three-dimensional figures

Learning Objectives Define what a net of a three-dimensional figure is. Identify valid nets for common three-dimensional figures such as cubes, prisms, and pyramids. Draw a net for a given three-dimensional figure with specified dimensions. Visualize how a two-dimensional net folds into its corresponding three-dimensional figure. Determine if a given two-dimensional pattern is a valid net for a specific three-dimensional figure. Calculate the surface area of a three-dimensional figure using its net. Ever wondered how a flat piece of cardboard can turn into a sturdy box or a cool paper craft? 📦 In this lesson, you'll discover how to 'unfold' three-dimensional shapes into two-dimensional patterns called nets. Understanding nets helps us visualize the structure...

TermDefinitionExample Three-Dimensional (3D) FigureAn object that has length, width, and height, occupying space. Also known as a solid figure.A cube, a rectangular prism, a pyramid, a cylinder. NetA two-dimensional (2D) pattern that can be folded along its edges to form a three-dimensional (3D) figure without any overlaps or gaps.A cross shape made of six squares is a common net for a cube. FaceA flat surface of a three-dimensional figure.A cube has 6 square faces; a rectangular prism has 6 rectangular faces. EdgeA line segment where two faces of a three-dimensional figure meet.A cube has 12 edges; a triangular prism has 9 edges. VertexA point where three or more edges of a three-dimensional figure meet.A cube has 8 vertices; a square pyramid has 5 vertices. PrismA three-dimensional figu...

Rule for Valid Nets A valid net must contain all the faces of the 3D figure, connected in a way that allows them to fold up perfectly without overlapping or leaving gaps. When designing or identifying a net, ensure that every face of the target 3D figure is represented and that their connections allow for a complete, solid shape when folded. Surface Area Calculation from a Net The total surface area ($SA$) of a 3D figure is the sum of the areas of all the individual faces in its net: $SA = \sum \text{Area of each face}$ To find the surface area of a 3D figure, first identify its net. Then, calculate the area of each distinct 2D shape (face) in the net and add all these areas together. Euler's Formula for Polyhedra $V - E + F = 2$ For any convex polyhedron (like...