Net (3D Figure)
In short: A net of a 3D figure lays every face of a solid flat in one connected piece, so that folding along the joins rebuilds a cube, prism or pyramid.
6th GradeGeometry6.G.A.4
What is Net?
Take a cardboard box apart along its seams and press it flat: you get a net of a 3D figure. Every face of the solid appears once, and the faces are joined along edges that become folds.
Precisely, a net for a prism has two congruent bases and rectangles for the sides; a net for a pyramid has one base and triangles. The total area of a net equals the surface area of the solid, and one solid can have several different valid nets.
How to spot it
- A drawing shows connected squares, rectangles or triangles in a cross, strip or staircase pattern.
- A question asks which flat pattern is a valid net of a 3D figure such as a given box or pyramid.
- You are asked to count faces or find the total area of the wrapping material.
- A package designer needs the template that is cut from one sheet.
The method
- Count the faces and list their shapes and sizes before drawing anything.
- Draw them joined edge to edge so that every fold keeps the faces from overlapping when closed.
- Check that matching sides meet when folded: edges that meet in the solid must be the same length.
- Add every face of the net to get the surface area of the solid it folds into.
Net: solved example
Problem
A net for a box has two faces of 6 in. by 4 in., two faces of 6 in. by 3 in. and two faces of 4 in. by 3 in. How much cardboard does the net use?
Solution
Face areas: \(6 \cdot 4 = 24\), \(6 \cdot 3 = 18\) and \(4 \cdot 3 = 12\), each appearing twice.
Total: \(2(24 + 18 + 12) = 2 \cdot 54 = 108\). The net uses 108 square inches of cardboard.
Try it
Question 1
How many faces does a net of a triangular pyramid have?
Show the answer
Four triangles: one base and three sides.
Question 2
A net has six squares of side 2 cm. Find the area of the net.
Show the answer
\(6 \cdot 4 = 24\) square centimeters.
Net vs. Surface Area
A net of a 3D figure is the flat drawing of the faces. The surface area is the number you get by adding the areas of the faces shown in that drawing. Different nets of the same solid always give the same surface area.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · 6th Grade · Geometry