Volume of triangular prism base 12 height 5 length 9

Step by step

The question

Question: find the volume of a triangular prism with triangle base 12 and height 5, and length 9.

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 × 12 × 5.

12 times 5 is 60.

That is the whole box.

Half of 60 means 60 divided by 2.

That is 30.

So the base is A = 30 square units.

2 Base times length

The prism is that triangle, stacked up 9 long.

So the volume is V = A × length.

Now put the numbers in: A = 30 and length = 9.

30 times 9 is 270.

So the volume is 270 cubic units.

Let's look back.

First: area of the base.

Last: base times length.