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
![**Educational Content on Surface Area of a Square-Based Pyramid**
**Diagram Explanation:**
The image includes a representation of a square-based pyramid with the following dimensions:
- Base length: 7 meters
- Slant height: 11 meters
The diagram shows a 3D pyramid model with its base and slant height labeled for better understanding.
**Question:**
What is the surface area of the square-based pyramid shown? (Round to the nearest whole number)
**Answer Choices:**
- 147
- 360
- 220
- 203
**Solution:**
1. **Calculate the area of the base:**
The base is a square, so its area can be calculated as:
\[
\text{Area of the base} = \text{side}^2 = 7 \, \text{m} \times 7 \, \text{m} = 49 \, \text{m}^2
\]
2. **Calculate the area of one of the triangular faces:**
Each triangular face has a base equal to the side of the square base and a height equal to the slant height of the pyramid. The area of one triangular face can be calculated as:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \, \text{m} \times 11 \, \text{m} = 38.5 \, \text{m}^2
\]
3. **Calculate the total area of the four triangular faces:**
There are four identical triangular faces, so their total area is:
\[
\text{Total area of four triangles} = 4 \times 38.5 \, \text{m}^2 = 154 \, \text{m}^2
\]
4. **Add the area of the base and the total area of the triangular faces:**
\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of four triangles} = 49 \, \text{m}^2 + 154 \, \text{m}^2 = 203 \, \text{m}^2
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34dbf93a-185c-4522-bbbf-f73f18b87311%2F566d45e9-9a56-463d-8bfc-efb46553b128%2Fy9namhll_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content on Surface Area of a Square-Based Pyramid**
**Diagram Explanation:**
The image includes a representation of a square-based pyramid with the following dimensions:
- Base length: 7 meters
- Slant height: 11 meters
The diagram shows a 3D pyramid model with its base and slant height labeled for better understanding.
**Question:**
What is the surface area of the square-based pyramid shown? (Round to the nearest whole number)
**Answer Choices:**
- 147
- 360
- 220
- 203
**Solution:**
1. **Calculate the area of the base:**
The base is a square, so its area can be calculated as:
\[
\text{Area of the base} = \text{side}^2 = 7 \, \text{m} \times 7 \, \text{m} = 49 \, \text{m}^2
\]
2. **Calculate the area of one of the triangular faces:**
Each triangular face has a base equal to the side of the square base and a height equal to the slant height of the pyramid. The area of one triangular face can be calculated as:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \, \text{m} \times 11 \, \text{m} = 38.5 \, \text{m}^2
\]
3. **Calculate the total area of the four triangular faces:**
There are four identical triangular faces, so their total area is:
\[
\text{Total area of four triangles} = 4 \times 38.5 \, \text{m}^2 = 154 \, \text{m}^2
\]
4. **Add the area of the base and the total area of the triangular faces:**
\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of four triangles} = 49 \, \text{m}^2 + 154 \, \text{m}^2 = 203 \, \text{m}^2
\
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