Pyramids

The idea

A pyramid has a polygonal base and a point outside it joined by edges to each vertex of the base; it is named by its base, and a triangular pyramid is also called a tetrahedron.

A tent and a roof

Think of the roof of a tower or a tent that comes to a point. It sits on a square and rises to one point at the top.

How many sloping triangles meet at the point?

• 3
• 4
• 5

Build a pyramid

Choose a polygon. Use Lift point to raise the orange point out of it. Then tap each dotted line to join a corner of the polygon to the point.

A polygon and a point

A pyramid has a polygonal base and a point outside it, and edges connect the point with each of the vertices of the base. It is named by its base: a triangular pyramid, a square pyramid, a pentagonal pyramid, and so on. A triangular pyramid is also known as a tetrahedron.

Every side of the base gives one triangle between the base and the point.

Add the base to the triangles to get all the faces. A triangular pyramid has 4 faces, all triangles: it is a tetrahedron.

• Base | Name | Triangles
• Triangle | Triangular pyramid | 3
• Square | Square pyramid | 4
• Pentagon | Pentagonal pyramid | 5
• Hexagon | Hexagonal pyramid | 6

Notes

A pyramid has a polygonal base and a point outside it, joined by edges to every vertex of the base. It is named by its base, like a square pyramid. A triangular pyramid is also called a tetrahedron.

Check yourself

The base of a pyramid is a hexagon. How many edges join the point to the corners of the base?

Answer: 6 edges

There is one edge from the point to each of the 6 vertices of the hexagon: 6 edges. With the 6 edges of the base, the pyramid has 12 edges in all.

Which of these solids is a pyramid?

How many faces in all does this pentagonal pyramid have?

Answer: 6 faces

5 triangles + 1 pentagon = 6 faces.

Which solid is also called a tetrahedron?

• Solid A — correct. Yes! A has a square base and one point joined to all four corners. The point is not over the middle, but a pyramid only needs the point to be outside the base.
• Solid B. B has two pentagons that are the same, joined by parallelograms. That is a prism.
• Solid C. C has a small square at the top. There is no single point that the edges meet at.
• A square pyramid. A square pyramid has a square base and 4 triangles. The tetrahedron is the pyramid on a triangle.
• A triangular prism. A triangular prism has two triangles joined by 3 parallelograms. It is not a pyramid.
• A triangular pyramid — correct. Yes! A triangular pyramid is also known as a tetrahedron. It has 4 faces, and all of them are triangles.