How to Find Prism Volume?

To find the volume of a prism, you need to multiply the area of its base by its height.

Understanding the Prism Volume Formula

The formula for calculating the volume (V) of any prism is quite straightforward:

V = B × h

Where:

V represents the volume of the prism.
B represents the area of the base of the prism.
h represents the height of the prism (the perpendicular distance between the two bases).

Here's a step-by-step guide to calculating the volume of a prism:

Identify the Base: Determine the shape of the prism's base. This could be a triangle, square, rectangle, pentagon, or any other polygon. Both the top and bottom of a prism are its bases.
Calculate the Area of the Base (B):
- Triangle: Use the formula (1/2) × base × height.
- Square: Use the formula side × side, or side².
- Rectangle: Use the formula length × width.
- Other Polygons: Use the appropriate formula for the base. If the polygon is complex, you may need to break it into simpler shapes.
Determine the Height (h): Identify the perpendicular distance between the two bases of the prism.
Multiply: Multiply the area of the base (B) by the height of the prism (h).

Example 1: Rectangular Prism
- Imagine a rectangular prism with a base that is 5 cm long and 3 cm wide, and a height of 10 cm.
- Area of the base (B) = 5 cm × 3 cm = 15 cm²
- Volume (V) = 15 cm² × 10 cm = 150 cm³
Example 2: Triangular Prism
- Imagine a triangular prism with a base that has a base of 6 cm and a height of 4 cm. The prism has a height of 12 cm.
- Area of the base (B) = (1/2) × 6 cm × 4 cm = 12 cm²
- Volume (V) = 12 cm² × 12 cm = 144 cm³

The height (h) must always be perpendicular to the bases of the prism.
The units of volume are always cubic (e.g., cm³, m³, ft³).
This formula applies to all types of prisms, regardless of the shape of their base.