What is the lateral area of the pyramid shown below? Lateral Area Pyramid = PL P Square= 4s; s = side length Use the pythagorean theorem to solve for slant heigh, L 10² + L²=26² 26 ft. 20 ft
What is the lateral area of the pyramid shown below? Lateral Area Pyramid = PL P Square= 4s; s = side length Use the pythagorean theorem to solve for slant heigh, L 10² + L²=26² 26 ft. 20 ft
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
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![## Calculating the Lateral Area of a Pyramid
**Problem Statement:**
What is the lateral area of the pyramid shown below?
**Lateral Area Formula:**
\[ \text{Lateral Area}_{\text{Pyramid}} = \frac{1}{2} PL \]
Where:
- \( P \) is the perimeter of the base.
- \( L \) is the slant height.
**Perimeter for a Square Base:**
\[ P_{\text{Square}} = 4s \]
\( s = \) side length of the square base.
**Given Dimensions:**
- Side length of the base (\( s \)) = 20 ft.
- Height of the pyramid (Vertical height from the center of the base to the apex) = 10 ft.
- Slant height (\( L \)) = 26 ft.
**Finding the Slant Height:**
We are asked to use the Pythagorean theorem to solve for the slant height, \( L \):
\[ 10^2 + L^2 = 26^2 \]
**Steps:**
1. **Calculate the Perimeter of the Base:**
\[ P = 4 \times 20 = 80 \, \text{ft} \]
2. **Solve for \( L \) Using the Pythagorean Theorem:**
\[ 10^2 + L^2 = 26^2 \]
\[ 100 + L^2 = 676 \]
\[ L^2 = 576 \]
\[ L = \sqrt{576} \]
\[ L = 24 \, \text{ft} \]
3. **Calculate the Lateral Area:**
\[ \text{Lateral Area}_{\text{Pyramid}} = \frac{1}{2} \times P \times L \]
\[ \text{Lateral Area}_{\text{Pyramid}} = \frac{1}{2} \times 80 \times 24 \]
\[ \text{Lateral Area}_{\text{Pyramid}} = 960 \, \text{ft}^2 \]
Therefore, the lateral area of the pyramid is \( 960 \, \text{ft}^2 \).
**Diagram Explanation:**
The diagram shows a pyramid with a square base. The side length of the base is 20 ft, and the height from the center of the base to the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95b555fe-c61f-4380-ac77-d5f60f2cc03d%2Fa2e427cb-6c48-4d16-aaf6-b250be20818f%2Fmnwc7u8_processed.png&w=3840&q=75)
Transcribed Image Text:## Calculating the Lateral Area of a Pyramid
**Problem Statement:**
What is the lateral area of the pyramid shown below?
**Lateral Area Formula:**
\[ \text{Lateral Area}_{\text{Pyramid}} = \frac{1}{2} PL \]
Where:
- \( P \) is the perimeter of the base.
- \( L \) is the slant height.
**Perimeter for a Square Base:**
\[ P_{\text{Square}} = 4s \]
\( s = \) side length of the square base.
**Given Dimensions:**
- Side length of the base (\( s \)) = 20 ft.
- Height of the pyramid (Vertical height from the center of the base to the apex) = 10 ft.
- Slant height (\( L \)) = 26 ft.
**Finding the Slant Height:**
We are asked to use the Pythagorean theorem to solve for the slant height, \( L \):
\[ 10^2 + L^2 = 26^2 \]
**Steps:**
1. **Calculate the Perimeter of the Base:**
\[ P = 4 \times 20 = 80 \, \text{ft} \]
2. **Solve for \( L \) Using the Pythagorean Theorem:**
\[ 10^2 + L^2 = 26^2 \]
\[ 100 + L^2 = 676 \]
\[ L^2 = 576 \]
\[ L = \sqrt{576} \]
\[ L = 24 \, \text{ft} \]
3. **Calculate the Lateral Area:**
\[ \text{Lateral Area}_{\text{Pyramid}} = \frac{1}{2} \times P \times L \]
\[ \text{Lateral Area}_{\text{Pyramid}} = \frac{1}{2} \times 80 \times 24 \]
\[ \text{Lateral Area}_{\text{Pyramid}} = 960 \, \text{ft}^2 \]
Therefore, the lateral area of the pyramid is \( 960 \, \text{ft}^2 \).
**Diagram Explanation:**
The diagram shows a pyramid with a square base. The side length of the base is 20 ft, and the height from the center of the base to the
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