Step by step
The question
Question: what shape is the cut, if we slice a box 10 by 3 by 7 parallel to the base, and what is its area?
box 10 by 3 by 7, cut parallel to the base
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 box.
We slice it parallel to the base.
The red face is the cut.
2 Name the shape
Flat, the cut looks like this.
The cut is the same as the bottom face: a rectangle.
So it is a rectangle.
= cut: a rectangle 10 by 3
Careful!
A cut parallel to the base always has the shape of the base.
Careful: parallel cut = the base shape
3 Find its area
A rectangle's area is length times width: 30.
= area = 10 × 3 = 30
4 Check
Let's check: a cut parallel to the base has the shape of the base.
So the answer is right!
like the base: rectangle
Let's look back.
First: look at the cut.
Then: name the shape.
Then: find its area.
Last: check.
Answer
= area = 10 × 3 = 30