The volume of any prism is the area of its base times its height.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why that works
A prism is the same shape stacked up. Each layer holds the base area, and there are height layers.
With a triangular base
Find the triangle area first, then multiply by the length of the prism.
Surface area
Add the two ends and every rectangular side. A net makes none of them easy to miss.
Base area times height, whatever the base
A prism has the same cross-section all the way along, so its volume is the area of that cross-section times the length. This works for triangular, hexagonal or any other prism — not just boxes.
Identify the base first
The base is the repeating cross-section, which is not always the face at the bottom. For a prism lying on its side, the base is one of the ends. Getting the base right is most of the work; the multiplication is trivial.
Surface area from the net
Unfold the prism: two copies of the base, plus a rectangle for each side face. Or note that all the side faces together form one rectangle whose width is the base's perimeter. That shortcut saves a lot of arithmetic.
Cubic against square
Volume is cubic units, surface area square units. Two different questions about the same solid, exactly as with area and perimeter in two dimensions. The units are the fastest way to check which you have computed.
Step 2: Try It Yourself
Tap and try it out.
- Cubes in one layer4 × 3 = 12
- Layers3
- 4 × 3 × 336 cubic units
Counting every cube gives 36, and so does 4 × 3 × 3. The formula is a shortcut for the count.
Step 3: Watch an Example
One step at a time.
Watch Leo Find a Triangular Prism Volume
A prism has a triangular base with base 6 and height 4, and a length of 10.
- Step 1
He finds the area of the triangle: half of 6 × 4, which is 12.
Step 4: Your Turn
Practice makes it stick.
The Tent
Problem 1 of 2
A triangular base of area 15 and a length of 8. What is the volume?
cubic units
The Box
Problem 2 of 2
A box 6 by 4 by 5. What is the volume?
cubic units
Stack the Base
1 of 4
Base area 20, height 6. Volume?
2 of 4
Triangle base 8, triangle height 5. What is the base area?
3 of 4
Base area 12, height 9. Volume?
4 of 4
A cube with edge 4. Volume?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Base area 18, height 7. Volume?
Question 2 of 2
What is the volume of any prism?
What You Learned
- Volume of a prism is base area times height.
- The base can be any shape.
- Surface area adds the two ends and every side.