Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![## Finding the Volume of a Triangular Prism
To find the volume of a triangular prism, you can use the formula:
\[ V = \text{Base Area} \times \text{Height} \]
### Given Information:
- The measures shown in the diagram are:
- The height of the triangular face (\(h\)) is 4 units.
- The base of the triangular face (\(b\)) is 3 units.
- The length of the prism (depth or the distance between the triangular faces) (\(l\)) is 2 units.
### Steps to Calculate the Volume:
1. **Calculate the Area of the Triangular Base:**
The area \(A\) of a triangle is given by:
\[ A = \frac{1}{2} \times b \times h \]
where \(b\) is the base and \(h\) is the height of the triangle.
Plugging in the given values:
\[ A = \frac{1}{2} \times 3 \times 4 = 6 \, \text{square units} \]
2. **Calculate the Volume of the Prism:**
Using the volume formula \(V = \text{Base Area} \times \text{Height} \):
\[ V = 6 \, \text{square units} \times 2 \, \text{units} = 12 \, \text{cubic units} \]
So, the volume of the triangular prism is \(12\) cubic units.
### Diagram Explanation:
The diagram shows a triangular prism with:
- A triangular base with height 4 units and base 3 units.
- The depth (length) of the prism is 2 units.
By following the above steps using the dimensions provided, you can successfully calculate the volume of the triangular prism.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff43659e0-f89c-4c75-b147-c505b3ac3c78%2Fee1cbe8e-f220-4501-8839-065a4297b12f%2Fveqjid_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Finding the Volume of a Triangular Prism
To find the volume of a triangular prism, you can use the formula:
\[ V = \text{Base Area} \times \text{Height} \]
### Given Information:
- The measures shown in the diagram are:
- The height of the triangular face (\(h\)) is 4 units.
- The base of the triangular face (\(b\)) is 3 units.
- The length of the prism (depth or the distance between the triangular faces) (\(l\)) is 2 units.
### Steps to Calculate the Volume:
1. **Calculate the Area of the Triangular Base:**
The area \(A\) of a triangle is given by:
\[ A = \frac{1}{2} \times b \times h \]
where \(b\) is the base and \(h\) is the height of the triangle.
Plugging in the given values:
\[ A = \frac{1}{2} \times 3 \times 4 = 6 \, \text{square units} \]
2. **Calculate the Volume of the Prism:**
Using the volume formula \(V = \text{Base Area} \times \text{Height} \):
\[ V = 6 \, \text{square units} \times 2 \, \text{units} = 12 \, \text{cubic units} \]
So, the volume of the triangular prism is \(12\) cubic units.
### Diagram Explanation:
The diagram shows a triangular prism with:
- A triangular base with height 4 units and base 3 units.
- The depth (length) of the prism is 2 units.
By following the above steps using the dimensions provided, you can successfully calculate the volume of the triangular prism.
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