Prisms

The idea

A prism has two congruent polygons as opposite faces, with edges connecting their corresponding vertices, and all other faces are parallelograms; it is named by the polygon, as a triangular or pentagonal prism.

A hexagonal pencil

Look at a new hexagonal pencil. Both of its ends are the same hexagon, and flat strips run along its length.

How many flat strips run along the pencil?

• 4
• 6
• 8

Build a prism

Choose a polygon. Use Lift copy to raise an exact copy of it. Then tap each dotted line to join a corner to its matching corner. Drag the picture to look from the other side.

Two polygons and parallelograms

A prism has two congruent polygons as opposite faces, with edges connecting the corresponding vertices of these polygons. All the other faces are parallelograms. It is named by its polygon: a triangular prism, a pentagonal prism, and so on.

Every side of the polygon gives one parallelogram.

Add the two ends to the side faces to get all the faces of the prism.

• Two ends | Name | Side faces
• Triangles | Triangular prism | 3
• Squares | Square prism | 4
• Pentagons | Pentagonal prism | 5
• Hexagons | Hexagonal prism | 6

Notes

A prism has two congruent polygons as opposite faces, joined corner to matching corner by edges. All the other faces are parallelograms. It is named by its polygon, like a pentagonal prism.

Check yourself

The two ends of a prism are octagons (8 sides each). How many parallelogram faces go round its sides?

Answer: 8 faces

One parallelogram for each of the 8 sides of the octagon: 8 faces. With the 2 octagon ends, the prism has 10 faces in all.

Which of these solids is a prism?

How many faces in all does this pentagonal prism have?

Answer: 7 faces

5 parallelograms + 2 pentagons = 7 faces.

Meena pushes the top of a prism sideways, so it leans. She says, "It is not a prism any more." What do you say?

• Solid A. A has one polygon, a hexagon at the bottom, and a point at the top. A prism needs two congruent polygons as opposite faces.
• Solid B. B has a small square at the top and a bigger square at the bottom. They are not congruent, and the faces between them are not parallelograms.
• Solid C — correct. Yes! C has two pentagons that are the same, joined by parallelograms. It leans, but it is still a prism.
• She is wrong. The two ends are still congruent polygons and the other faces are still parallelograms. — correct. Yes! Pushing the top sideways changes neither end, and the side faces stay parallelograms. That is all a prism needs.
• She is right. The side faces are no longer rectangles.. A prism does not need rectangles. It needs its other faces to be parallelograms.
• She is right. It has turned into a pyramid.. A pyramid has one polygon and a point. This solid still has two polygons.