Volume of triangular prism base 4 height 3 length 10

Step by step

The question

Question: find the volume of a triangular prism with triangle base 4 and height 3, and length 10.

1 Area of the base

A prism has the same shape all the way through.

Here it is a triangle.

The triangle is the base.

Careful: the prism lies on its side.

Its base is the triangle at the end, not the face it lies on.

The triangle is half of the box around it.

So its area is half of base times height: A = ½ × 4 × 3.

4 times 3 is 12.

That is the whole box.

Half of 12 means 12 divided by 2.

That is 6.

So the base is A = 6 square units.

2 Base times length

The prism is that triangle, stacked up 10 long.

So the volume is V = A × length.

Now put the numbers in: A = 6 and length = 10.

6 times 10 is 60.

So the volume is 60 cubic units.

Let's look back.

First: area of the base.

Last: base times length.