Nets of three-dimensional solids

In the following it is a good idea to use paper to form the nets.

Question 1

Which net when folded makes a triangular-based pyramid?

4 different net shapes of triangular-base pyramids

Detailed description of diagram

Solution

The faces of a pyramid, other than the base face, are triangles.

Here are pictures of 3 different types of pyramids.

three 3D pyramid shapes
Detailed description of diagram

square-based pyramid

hexagonal-based pyramid

triangular-based pyramid

It can only be the second or the fourth net.
Looking at the drawing of the triangular–based prism we see that that the number of edges/faces meeting at a vertex is 3. The second net has 4 faces meeting at a vertex. So the fourth net must be the one that makes a triangular-based pyramid.

When a triangular-based pyramid has all of its triangular faces the same (congruent) it is called a tetrahedron.

Possible nets for a tetrahedron

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