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 the Surface Area of a Square Pyramid**
**Introduction:**
This lesson focuses on finding the surface area of a square pyramid. The square pyramid in question has a side length of 3 miles and a slant height of 3 miles. Understanding how to calculate the surface area is important for various practical applications, including construction and design.
---
**Problem Statement:**
*Find the surface area of a square pyramid with side length 3 miles and slant height 3 miles.*
---
**Diagram Explanation:**
In the provided image, a square pyramid is depicted. The base of the pyramid is a square with each side measuring 3 miles. The slant height, which is the distance from the middle of one side of the base to the apex of the pyramid, is also 3 miles. The diagram labels the side length and slant height for clarity.
---
**Key Concepts:**
To calculate the surface area of a square pyramid, you need to consider both the base area and the area of the triangular faces. The formula for the surface area \(A\) of a square pyramid is given by:
\[ A = B + L \]
where \(B\) is the area of the base and \(L\) is the lateral surface area. Here are the steps to find each component:
1. **Area of the Base (B):**
Since the base is a square:
\[
B = \text{side length}^2 = 3^2 = 9 \ \text{mi}^2
\]
2. **Lateral Surface Area (L):**
There are four triangular faces, each with a base of 3 miles and a slant height of 3 miles. The area of one triangular face is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 3 \times 3 = 4.5 \ \text{mi}^2
\]
For four triangles:
\[
L = 4 \times \text{Area of one triangle} = 4 \times 4.5 = 18 \ \text{mi}^2
\]
3. **Total Surface Area (A):**
\[
A = B + L =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe95140d0-b0ae-4b73-878d-570406dc1277%2F2a378fd5-b579-42fb-92f3-0e0f4685f91c%2Feswf6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Surface Area of a Square Pyramid**
**Introduction:**
This lesson focuses on finding the surface area of a square pyramid. The square pyramid in question has a side length of 3 miles and a slant height of 3 miles. Understanding how to calculate the surface area is important for various practical applications, including construction and design.
---
**Problem Statement:**
*Find the surface area of a square pyramid with side length 3 miles and slant height 3 miles.*
---
**Diagram Explanation:**
In the provided image, a square pyramid is depicted. The base of the pyramid is a square with each side measuring 3 miles. The slant height, which is the distance from the middle of one side of the base to the apex of the pyramid, is also 3 miles. The diagram labels the side length and slant height for clarity.
---
**Key Concepts:**
To calculate the surface area of a square pyramid, you need to consider both the base area and the area of the triangular faces. The formula for the surface area \(A\) of a square pyramid is given by:
\[ A = B + L \]
where \(B\) is the area of the base and \(L\) is the lateral surface area. Here are the steps to find each component:
1. **Area of the Base (B):**
Since the base is a square:
\[
B = \text{side length}^2 = 3^2 = 9 \ \text{mi}^2
\]
2. **Lateral Surface Area (L):**
There are four triangular faces, each with a base of 3 miles and a slant height of 3 miles. The area of one triangular face is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 3 \times 3 = 4.5 \ \text{mi}^2
\]
For four triangles:
\[
L = 4 \times \text{Area of one triangle} = 4 \times 4.5 = 18 \ \text{mi}^2
\]
3. **Total Surface Area (A):**
\[
A = B + L =
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning