Volume of triangular prism sides 5, 12, 13 length 10

Step by step

The question

Question: find the volume of a triangular prism with triangle sides 5, 12 and 13, 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.

Is there a right angle?

5 squared plus 12 squared is 25 plus 144, which is 169.

That is 13 squared.

So yes: the triangle has a right angle.

So its two short sides are its base and height: 12 and 5.

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 10 long.

So the volume is V = A × length.

Now put the numbers in: A = 30 and length = 10.

30 times 10 is 300.

So the volume is 300 cubic units.

Let's look back.

First: area of the base.

Last: base times length.