Volume of triangular prism base 3 height 5 length 2.4

Step by step

The question

Question: find the volume of a triangular prism with triangle base 3 and height 5, and length 2.4.

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 × 3 × 5.

3 times 5 is 15.

That is the whole box.

Half of 15 means 15 divided by 2.

That is 7.5.

So the base is A = 7.5 square units.

2 Base times length

The prism is that triangle, stacked up 2.4 long.

So the volume is V = A × length.

Now put the numbers in: A = 7.5 and length = 2.4.

Forget the points: 75 times 24 is 1800.

Together, the numbers have 1 + 1 = 2 digits after the point.

So the answer has 2 too: 18.00, which is 18.

So the volume is 18 cubic units.

Let's look back.

First: area of the base.

Last: base times length.