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Slice a square pyramid through the top, up and down

Step by step, with the reason for every step · Cross sections · Geometry

Step by step

The question

Question: what shape is the cut, if we slice a square pyramid through the top, up and down?

square pyramid, cut through the top, up and down

A cross section is the flat face we see when we slice a solid.

cross section = the face of a cut

1 Look at the cut

Here is the square pyramid.

We slice it through the top, up and down.

The red face is the cut.

2 Name the shape

Flat, the cut looks like this.

Up and down through the top: the cut is a triangle.

So it is a triangle.

= cut: a triangle

Careful!

Not a square.

Only a cut straight across shows the square base.

Careful: not a square ✗

3 Check

Let's check: look at the square pyramid from the side.

You see a triangle, the same as the cut through the middle.

So the answer is right!

side view: triangle

Let's look back.

First: look at the cut.

Then: name the shape.

Last: check.

Answer
Careful: not a square ✗

Your turn

Try this one yourself, then check:

cone, cut parallel to the base
Show the answer
a circle

More from Cross sections

The whole lesson: Cross sections →