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
Related questions
Question
![### Finding the Volume of a Triangular Prism
To calculate the volume of a triangular prism, follow the steps below. Be sure to include the correct unit in your final answer.
#### Steps:
1. **Find the Area of the Triangular Base:**
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
From the diagram, the base and height of the triangular base are both 8 feet.
\[
\text{Area} = \frac{1}{2} \times 8 \, \text{ft} \times 8 \, \text{ft} = 32 \, \text{ft}^2
\]
2. **Calculate the Volume of the Prism:**
The volume of a prism is found using the formula:
\[
\text{Volume} = \text{Base Area} \times \text{length (or height) of the prism}
\]
From the diagram, the length of the prism is 7 feet.
\[
\text{Volume} = 32 \, \text{ft}^2 \times 7 \, \text{ft} = 224 \, \text{ft}^3
\]
Therefore, the volume of the triangular prism is **224 cubic feet (224 ft³)**.
#### Diagram Explanation:
The diagram shows a triangular prism with dimensions labeled:
- The base and height of the triangular base are both 8 feet.
- The length of the prism (distance between the triangular bases) is 7 feet.
Ensure your answer is accompanied by the appropriate unit of volume, in this case, cubic feet (ft³).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F550c2c8a-e869-4cc2-9338-8dc4995fc738%2Fc9a7d221-e199-4d3c-9538-d0682bb160d3%2Fb1907pq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Volume of a Triangular Prism
To calculate the volume of a triangular prism, follow the steps below. Be sure to include the correct unit in your final answer.
#### Steps:
1. **Find the Area of the Triangular Base:**
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
From the diagram, the base and height of the triangular base are both 8 feet.
\[
\text{Area} = \frac{1}{2} \times 8 \, \text{ft} \times 8 \, \text{ft} = 32 \, \text{ft}^2
\]
2. **Calculate the Volume of the Prism:**
The volume of a prism is found using the formula:
\[
\text{Volume} = \text{Base Area} \times \text{length (or height) of the prism}
\]
From the diagram, the length of the prism is 7 feet.
\[
\text{Volume} = 32 \, \text{ft}^2 \times 7 \, \text{ft} = 224 \, \text{ft}^3
\]
Therefore, the volume of the triangular prism is **224 cubic feet (224 ft³)**.
#### Diagram Explanation:
The diagram shows a triangular prism with dimensions labeled:
- The base and height of the triangular base are both 8 feet.
- The length of the prism (distance between the triangular bases) is 7 feet.
Ensure your answer is accompanied by the appropriate unit of volume, in this case, cubic feet (ft³).
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