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What is the lateral area of the pyramid shown below? 26 ft. 20 ft. IN # 13 M ... 20 ft.

What is the lateral area of the pyramid shown below? 26 ft. 20 ft. IN # 13 M ... 20 ft.

Elementary Geometry For College Students, 7e
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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what is the lateral area of the pyramid shown below? 

### Question 4 **Multiple Choice** **What is the lateral area of the pyramid shown below?** ![Pyramid Diagram](link-to-image) 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.
Transcribed Image Text:### Question 4 **Multiple Choice** **What is the lateral area of the pyramid shown below?** ![Pyramid Diagram](link-to-image) 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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