8.7 15 10 14. What is the Surface Area of this EQUILATERAL TRIANGULAR based prism? What is the Volume of this EQUILATERAL TRIANGULAR based prism?
8.7 15 10 14. What is the Surface Area of this EQUILATERAL TRIANGULAR based prism? What is the Volume of this EQUILATERAL TRIANGULAR based prism?
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
![### Equilateral Triangular Prism
#### Surface Area Calculation
For an equilateral triangular prism, the surface area \(A\) is calculated using the formula:
\[ A = 2 \times A_{\text{base}} + A_{\text{sides}} \]
where:
- \(A_{\text{base}}\) is the area of one triangular base.
- \(A_{\text{sides}}\) is the area of the three rectangular sides.
Given the side length of the triangle is 10 units:
- The height (\(h\)) of the equilateral triangle can be calculated using the formula:
\[ h = \frac{\sqrt{3}}{2} \times s \]
- The area of the equilateral triangle base is:
\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times s^2 \]
- Substituting \(s = 10\):
\[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.7 \text{ units} \]
\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.3 \text{ square units} \]
- There are two triangular bases:
\[ 2 \times A_{\text{base}} \approx 2 \times 43.3 = 86.6 \text{ square units} \]
Each rectangular side has a width of 10 units and a length of 15 units:
- The area of one rectangular side is:
\[ A_{\text{rectangular side}} = 10 \times 15 = 150 \text{ square units} \]
- There are three rectangular sides:
\[ A_{\text{sides}} = 3 \times 150 = 450 \text{ square units} \]
Thus, the total surface area is:
\[ A = 86.6 + 450 = 536.6 \text{ square units} \]
#### Volume Calculation
The volume \(V\) of the prism is calculated using the formula:
\[ V = A_{\text{base}} \times \text{height of the prism} \]
Given:
- The area of the base \(A_{\text{base}} \approx 43.3 \text{ square units}\)
- The height of the prism is 15 units.
Thus, the volume \(V\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862b9fa7-38ef-42ad-9314-e47236df3348%2Fcd4579a5-153d-4239-80af-88657b861adf%2Fcoizxia_processed.png&w=3840&q=75)
Transcribed Image Text:### Equilateral Triangular Prism
#### Surface Area Calculation
For an equilateral triangular prism, the surface area \(A\) is calculated using the formula:
\[ A = 2 \times A_{\text{base}} + A_{\text{sides}} \]
where:
- \(A_{\text{base}}\) is the area of one triangular base.
- \(A_{\text{sides}}\) is the area of the three rectangular sides.
Given the side length of the triangle is 10 units:
- The height (\(h\)) of the equilateral triangle can be calculated using the formula:
\[ h = \frac{\sqrt{3}}{2} \times s \]
- The area of the equilateral triangle base is:
\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times s^2 \]
- Substituting \(s = 10\):
\[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.7 \text{ units} \]
\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.3 \text{ square units} \]
- There are two triangular bases:
\[ 2 \times A_{\text{base}} \approx 2 \times 43.3 = 86.6 \text{ square units} \]
Each rectangular side has a width of 10 units and a length of 15 units:
- The area of one rectangular side is:
\[ A_{\text{rectangular side}} = 10 \times 15 = 150 \text{ square units} \]
- There are three rectangular sides:
\[ A_{\text{sides}} = 3 \times 150 = 450 \text{ square units} \]
Thus, the total surface area is:
\[ A = 86.6 + 450 = 536.6 \text{ square units} \]
#### Volume Calculation
The volume \(V\) of the prism is calculated using the formula:
\[ V = A_{\text{base}} \times \text{height of the prism} \]
Given:
- The area of the base \(A_{\text{base}} \approx 43.3 \text{ square units}\)
- The height of the prism is 15 units.
Thus, the volume \(V\
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning