Volume of triangular prism sides 6, 8, 10 length 7

Step by step

The question

Question: find the volume of a triangular prism with triangle sides 6, 8 and 10, and length 7.

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?

6 squared plus 8 squared is 36 plus 64, which is 100.

That is 10 squared.

So yes: the triangle has a right angle.

So its two short sides are its base and height: 8 and 6.

The triangle is half of the box around it.

So its area is half of base times height: A = ½ × 8 × 6.

8 times 6 is 48.

That is the whole box.

Half of 48 means 48 divided by 2.

That is 24.

So the base is A = 24 square units.

2 Base times length

The prism is that triangle, stacked up 7 long.

So the volume is V = A × length.

Now put the numbers in: A = 24 and length = 7.

24 times 7 is 168.

So the volume is 168 cubic units.

Let's look back.

First: area of the base.

Last: base times length.