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 Surface Area of Prisms**
In this activity, we will determine the surface area of different types of prisms. Round your answers to the nearest tenth if necessary.
### Prism Calculations
#### Prism 5:
This is a rectangular prism with the dimensions:
- Length: 18 units
- Width: 6 units
- Height: 8 units
To find the surface area \( SA \) of a rectangular prism, use the formula:
\[ SA = 2lw + 2lh + 2wh \]
where \( l \), \( w \), and \( h \) are the length, width, and height respectively.
#### Prism 6:
This is another rectangular prism with the dimensions:
- Length: 15 units
- Width: 13 units
- Height: 7 units
Use the same formula for the surface area of a rectangular prism:
\[ SA = 2lw + 2lh + 2wh \]
#### Prism 7:
This is a triangular prism with a right-angled triangle base. The dimensions are:
- Base of the triangle: 6 units
- Height of the triangle: 9 units
- Length of the prism: 10 units
To find the surface area of a triangular prism:
1. Find the area of the triangular base:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
2. Calculate the perimeter of the triangle.
3. Use the formula:
\[ SA = (\text{Perimeter of triangle} \times \text{length of prism}) + 2 \times \text{Area of triangular base} \]
#### Prism 8:
This is another triangular prism with a right-angled triangle base. The dimensions are:
- Base of the triangle: 4 units
- Height of the triangle: 7 units
- Length of the prism: 3 units
Follow the same steps outlined for Prism 7 to find the surface area.
---
Using these formulas and steps, you can calculate the surface area for each prism provided in the image. Use the formulas to plug in the respective dimensions, and don’t forget to round to the nearest tenth when necessary!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb602927-d5c2-4b17-99bc-cf43c066f5a5%2F055efa81-dccf-4e04-8ed4-5bbffaa44bf5%2Fis0oi5m_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Surface Area of Prisms**
In this activity, we will determine the surface area of different types of prisms. Round your answers to the nearest tenth if necessary.
### Prism Calculations
#### Prism 5:
This is a rectangular prism with the dimensions:
- Length: 18 units
- Width: 6 units
- Height: 8 units
To find the surface area \( SA \) of a rectangular prism, use the formula:
\[ SA = 2lw + 2lh + 2wh \]
where \( l \), \( w \), and \( h \) are the length, width, and height respectively.
#### Prism 6:
This is another rectangular prism with the dimensions:
- Length: 15 units
- Width: 13 units
- Height: 7 units
Use the same formula for the surface area of a rectangular prism:
\[ SA = 2lw + 2lh + 2wh \]
#### Prism 7:
This is a triangular prism with a right-angled triangle base. The dimensions are:
- Base of the triangle: 6 units
- Height of the triangle: 9 units
- Length of the prism: 10 units
To find the surface area of a triangular prism:
1. Find the area of the triangular base:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
2. Calculate the perimeter of the triangle.
3. Use the formula:
\[ SA = (\text{Perimeter of triangle} \times \text{length of prism}) + 2 \times \text{Area of triangular base} \]
#### Prism 8:
This is another triangular prism with a right-angled triangle base. The dimensions are:
- Base of the triangle: 4 units
- Height of the triangle: 7 units
- Length of the prism: 3 units
Follow the same steps outlined for Prism 7 to find the surface area.
---
Using these formulas and steps, you can calculate the surface area for each prism provided in the image. Use the formulas to plug in the respective dimensions, and don’t forget to round to the nearest tenth when necessary!
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