Step by step
The question
Question: find the volume of a triangular prism with triangle sides 3 cm, 4 cm and 5 cm, and length 8 cm.
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?
3 squared plus 4 squared is 9 plus 16, which is 25.
That is 5 squared.
So yes: the triangle has a right angle.
So its two short sides are its base and height: 4 cm and 3 cm.
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 cm².
2 Base times length
The prism is that triangle, stacked up 8 cm long.
So the volume is V = A × length.
Now put the numbers in: A = 6 and length = 8.
6 times 8 is 48.
We count cubes, so the unit is cm³.
So the volume is 48 cm³.
Let's look back.
First: area of the base.
Last: base times length.