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The formula for the volume of a prism equals Base Area * Height
The base area formula that is used will vary according to the shape of the base.
Here are a few base area formulas.
Base Area of a Square = Side^2
Base Area of a Rectangle = Length * Height
Base Area of Triangle = 1⁄2 Base*Height
Base Area of a Polygon = 1⁄2 a*p*h
Find the volume of a rectangular prism with a base of 6 by 7 units and a height of 9 units?
Step 1. Base Area = Length * width = 6*7*= 42
( use length*width because it is a rectangular prism)
Step 2. Next take Base Area * Height = 42*9 = 378 units cubed (volume is always cubed)
Now a prism can be have different shaped bases. The key to finding the volume is to find the base area formula for that shape and then multiply this by the height.
For example, if you had a triangle shaped prism you would use ½ base x length x height to find the volume of the triangular prism
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a= apothem which is a line segment from the center of the polygon to the midpoint of one of its sides.
p = perimeter
h = height
How to find the Volume of a Prism
Example problem 2
Find the volume of the rectangular prism 2 that has a length of 4 units, a width of 3 units, and a height of 5 units.
Step 1. Use the formula :Volume = Base area x Height
Step 1a: Find the area of the base, which is a rectangle WXYZ
Use Base Area formula of a rectangle Length*Width
Length = 4units and Width = 3 units
4*3 = 12 square units = Base Area
Step 2: Multiply the area of the base times the height.
Volume of a prism = Base Area x Height.
Area of the base = 12 and Height = 5
Volume of a prism = 12 x 5 = 60 cubic units
Volume of a Prism
Example problem 1 Find the volume of the triangular prism 1 that has a base of 8 units and a height of 6.9 units.
Step 1 Use the formula: Volume = Base area x Height
Step 1a: Find the area of the base, which is triangle ABC.
Base Area of a triangle =1/2 Base * Height
base = 8 units and height = 6.9 units
½ *8*6.9 = 27.6 square units = Base Area of the triangular
Step 2: Multiply the area of the base times the height for
the volume.
Volume = 27.6 x 10 = 276 cubic units
Triangular Prism 1
Prism 2
Example Problem 3
How to find the volume of a prism
Find the volume of a rectangular prism with a base of 6 by 7 units and a height of 9 units?
Step 1. Base Area = Length * width = 6*7*= 42
( use length*width because it is a rectangular prism)
Step 2. Next take the Base Area * Height = 42*9 = 378 units cubed (volume is always cubed)
Now a prism can be have different shaped bases. The key to finding the volume is to find the base area formula for that shape and then multiply this by the height.
Check here for a list of base area formulas
For example, if you had a triangle shaped prism you would use ½ base x length x height to find the volume of the triangular prism
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