Volume of Triangular Prism - Formula, Definition, Examples

The Volume of Triangular Prism is the total space inside a shape that has two triangle ends and three flat sides. You find this amount by multiplying the triangle's area by the long length of the shape. We write the final answer in cubic units like cubic centimeters or cubic inches.

What is the volume of a triangular prism?

A triangular prism is a solid shape that looks like a roof of a house or a slice of cake. It has two matching triangles on the ends and three flat rectangular sides. The volume of the triangular prism definition is simply how much stuff can fit inside this 3D shape.

Here are the parts of this shape:

• Two Bases: These are the two triangles at the ends.

• Three Sides: These are the flat rectangles that join the triangles.

• Five Faces: This is the total number of flat surfaces.

• Nine Edges: These are the straight lines where two sides meet.

• Six Corners: These are the sharp points on the shape.

When we talk about the volume, we mean the room inside. If you filled a tent with air, the volume tells you how much air is there. You don't always need a volume of triangular prism calculator if you know these parts.

Volume of triangular prism formula

To find the space inside, we use a math rule. The volume of triangular prism formula is:

Volume = Area of the triangle end × Length of the prism

Because the end is a triangle, we find its area first. The rule for a triangle is:

• Area = ½ × base × height

Now, we put it all together for the volume of triangular prism:

• Volume = (½ × base × height) × Length

Don't get the triangle's height mixed up with the prism's length! The triangle height is just for the flat end. The length is how far the shape stretches. 

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Volume of triangular prism calculator steps

You can find the answer quickly without a volume of triangular prism calculator by following these three easy steps. These steps help when you do a volume of triangular prism worksheet.

Step 1: Get the area of the triangle

Look at the triangle end. Find its bottom (base) and its height. Multiply them and then take half of that.

• Example: If the base is 4 and height is 6, half of $4 \times 6$ is 12.

Step 2: Find the long length

Look at how long the prism is. This is the distance between the two triangle ends.

• Example: The length is 10.

Step 3: Multiply the numbers

Multiply the triangle area from Step 1 by the length from Step 2.

• Example: $12 \times 10 = 120$.

Using a volume of triangular prism worksheet is a good way to practice. Just make sure all your numbers use the same units, like all inches or all centimeters.

Volume of triangular prism examples

Let's try some practice problems. These show how the Volume of Triangular Prism - Formula, Definition, Examples works in real life.

Example 1: The Paper Weight

A glass paper weight has a triangle base of 3 cm and a height of 4 cm. It is 5 cm long.

• Triangle Area: $½ \times 3 \times 4 = 6$

• Volume: $6 \times 5 = 30$ cubic cm.

Example 2: The Candy Box

A candy box is 10 inches long. The triangle end has a base of 4 inches and a height of 3 inches.

• Triangle Area: $½ \times 4 \times 3 = 6$

• Volume: $6 \times 10 = 60$ cubic inches.

Example 3: The Big Wedge

A wooden wedge has a triangle base of 8 cm and a height of 5 cm. Its length is 20 cm.

• Triangle Area: $½ \times 8 \times 5 = 20$

• Volume: $20 \times 20 = 400$ cubic cm.

Simple tips for students

Learning about the volume of triangular prism is easier with these tips. They help you avoid mistakes on your homework.

• Check the Ends: The two triangles must be exactly the same size.

• The "3" Rule: Always put a 3 at the end of your units ($m^3$). This means "cubic."

• Don't Forget the Half: When finding the triangle area, always remember to divide by 2.

• Shape Names: A volume of triangular prism definition just means the space inside a 3D triangle shape.

• Standing Up: If the prism is standing up, the length is called the "height of the prism." It's still the same number!

• Water Fill: Imagine filling the shape with water. The volume tells you exactly how much it holds.

By using these rules, you won't need a volume of triangular prism calculator every time. You can do the math yourself! Just remember to find the triangle area first. Then, multiply it by how long the shape is. That is the secret to getting the right answer every single time.

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