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
what is the lateral area of the pyramid shown below?
In the diagram, a pyramid is shown with its base edges labeled as 20 ft and slant height labeled as 26 ft.
**Hint**: \( LA = \frac{1}{2}PL \); \( P \) = perimeter of base, \( L \) = slant height
**Options:**
- A) \( 520 \, \text{ft}^2 \)
- B) \( 1920 \, \text{ft}^2 \)
- C) \( 2320 \, \text{ft}^2 \)
### Explanation
To solve for the lateral area (LA) of the pyramid:
1. **Find the perimeter (P) of the base**
Since each side of the square base is 20 ft, the perimeter \( P \) is calculated as:
\[
P = 4 \times 20 \, \text{ft} = 80 \, \text{ft}
\]
2. **Use the given slant height (L)**:
\[
L = 26 \, \text{ft}
\]
3. **Apply the formula for lateral area**:
\[
LA = \frac{1}{2}PL
\]
Substituting the values:
\[
LA = \frac{1}{2} \times 80 \, \text{ft} \times 26 \, \text{ft} = \frac{1}{2} \times 2080 \, \text{ft}^2 = 1040 \, \text{ft}^2
\]
Therefore, the lateral area of the pyramid is **1040 \, \text{ft}^2**. However, since the answers do not match this calculation, please verify the measurements and calculations.
Given answer choices, none correctly match the calculated \( 1040 \, \text{ft}^2 \). Double-checking the measurements in the figure might be necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2341670b-b058-481d-a7e7-89b8beb6d704%2F5ec80fc1-78fc-4044-9fb5-67152a767c90%2Fb07uin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 4
**Multiple Choice**
**What is the lateral area of the pyramid shown below?**
In the diagram, a pyramid is shown with its base edges labeled as 20 ft and slant height labeled as 26 ft.
**Hint**: \( LA = \frac{1}{2}PL \); \( P \) = perimeter of base, \( L \) = slant height
**Options:**
- A) \( 520 \, \text{ft}^2 \)
- B) \( 1920 \, \text{ft}^2 \)
- C) \( 2320 \, \text{ft}^2 \)
### Explanation
To solve for the lateral area (LA) of the pyramid:
1. **Find the perimeter (P) of the base**
Since each side of the square base is 20 ft, the perimeter \( P \) is calculated as:
\[
P = 4 \times 20 \, \text{ft} = 80 \, \text{ft}
\]
2. **Use the given slant height (L)**:
\[
L = 26 \, \text{ft}
\]
3. **Apply the formula for lateral area**:
\[
LA = \frac{1}{2}PL
\]
Substituting the values:
\[
LA = \frac{1}{2} \times 80 \, \text{ft} \times 26 \, \text{ft} = \frac{1}{2} \times 2080 \, \text{ft}^2 = 1040 \, \text{ft}^2
\]
Therefore, the lateral area of the pyramid is **1040 \, \text{ft}^2**. However, since the answers do not match this calculation, please verify the measurements and calculations.
Given answer choices, none correctly match the calculated \( 1040 \, \text{ft}^2 \). Double-checking the measurements in the figure might be necessary.
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