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
![**Title: Calculating Surface Area of a Rectangular Prism**
**Prompt:**
"Find the surface area of the rectangular prism."
**Diagram Explanation:**
The diagram provided shows a rectangular prism with the following dimensions:
- The length of the base is 8 feet.
- The width of the base is 4 feet.
- The height of the prism is 8 feet.
**Details of the Diagram Colors:**
- The top face of the prism is colored in blue.
- The front and back faces are colored in green.
- The side faces are colored in red.
**Submission Area:**
Below the diagram, there is a field labeled "Answer" for students to type their solution. After entering their answer in square feet (ft²), they can click on the "Submit Answer" button.
**Steps to Find the Surface Area:**
To find the surface area of the rectangular prism, you need to calculate the area of all six faces and sum them up.
1. **Top and Bottom Faces:**
Area of one face: \(8 \text{ ft} \times 4 \text{ ft} = 32 \text{ ft}^2\)
Since there are two such faces: \(2 \times 32 \text{ ft}^2 = 64 \text{ ft}^2\)
2. **Front and Back Faces:**
Area of one face: \(8 \text{ ft} \times 8 \text{ ft} = 64 \text{ ft}^2\)
Since there are two such faces: \(2 \times 64 \text{ ft}^2 = 128 \text{ ft}^2\)
3. **Side Faces:**
Area of one face: \(4 \text{ ft} \times 8 \text{ ft} = 32 \text{ ft}^2\)
Since there are two such faces: \(2 \times 32 \text{ ft}^2 = 64 \text{ ft}^2\)
**Total Surface Area:**
Sum of the areas of all faces:
\[64 \text{ ft}^2 + 128 \text{ ft}^2 + 64 \text{ ft}^2 = 256 \text{ ft}^2\]
Students should input the total surface area in the answer field as:
\[256](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d15f8fb-8330-48aa-8c9a-25a9c39c3e69%2Fde790dee-b505-4df0-beac-5d5840f6a9c9%2Fxt40dx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Surface Area of a Rectangular Prism**
**Prompt:**
"Find the surface area of the rectangular prism."
**Diagram Explanation:**
The diagram provided shows a rectangular prism with the following dimensions:
- The length of the base is 8 feet.
- The width of the base is 4 feet.
- The height of the prism is 8 feet.
**Details of the Diagram Colors:**
- The top face of the prism is colored in blue.
- The front and back faces are colored in green.
- The side faces are colored in red.
**Submission Area:**
Below the diagram, there is a field labeled "Answer" for students to type their solution. After entering their answer in square feet (ft²), they can click on the "Submit Answer" button.
**Steps to Find the Surface Area:**
To find the surface area of the rectangular prism, you need to calculate the area of all six faces and sum them up.
1. **Top and Bottom Faces:**
Area of one face: \(8 \text{ ft} \times 4 \text{ ft} = 32 \text{ ft}^2\)
Since there are two such faces: \(2 \times 32 \text{ ft}^2 = 64 \text{ ft}^2\)
2. **Front and Back Faces:**
Area of one face: \(8 \text{ ft} \times 8 \text{ ft} = 64 \text{ ft}^2\)
Since there are two such faces: \(2 \times 64 \text{ ft}^2 = 128 \text{ ft}^2\)
3. **Side Faces:**
Area of one face: \(4 \text{ ft} \times 8 \text{ ft} = 32 \text{ ft}^2\)
Since there are two such faces: \(2 \times 32 \text{ ft}^2 = 64 \text{ ft}^2\)
**Total Surface Area:**
Sum of the areas of all faces:
\[64 \text{ ft}^2 + 128 \text{ ft}^2 + 64 \text{ ft}^2 = 256 \text{ ft}^2\]
Students should input the total surface area in the answer field as:
\[256
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