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
![### Understanding the Surface Area of a Square Base Pyramid
**Problem Statement:**
A square base pyramid is shown below. What is the surface area?
**Diagram Explanation:**
The diagram depicts a square base pyramid. The dimensions given are:
- The length of each side of the square base is 27 mm.
- The slant height from the midpoint of one side of the square base to the apex of the pyramid is 35 mm.
**Detailed Steps to Solve for Surface Area:**
1. **Calculate the Base Area:**
The base of the pyramid is a square. The area of a square is calculated as:
\[
\text{Base Area} = \text{side length}^2 = 27 \times 27 = 729 \text{ mm}^2
\]
2. **Calculate the Lateral Surface Area:**
The lateral surface area consists of four triangular faces.
The area of one triangular face can be calculated using:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base of the triangle} \times \text{slant height}
\]
For the given pyramid,
\[
\text{Area of one triangle} = \frac{1}{2} \times 27 \times 35 = \frac{1}{2} \times 945 = 472.5 \text{ mm}^2
\]
Since there are four triangular faces,
\[
\text{Total Lateral Surface Area} = 4 \times 472.5 = 1890 \text{ mm}^2
\]
3. **Calculate the Total Surface Area:**
The total surface area of the pyramid is the sum of the base area and the lateral surface area:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Surface Area} = 729 + 1890 = 2619 \text{ mm}^2
\]
**Final Answer:**
The surface area of the square base pyramid is \(2619 \text{ mm}^2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcd91cf-c92a-4a76-9c9a-e8d21c0f504d%2F51b31d0d-06cc-4619-8ba3-1f81450a7d2a%2Fq7s8a8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Surface Area of a Square Base Pyramid
**Problem Statement:**
A square base pyramid is shown below. What is the surface area?
**Diagram Explanation:**
The diagram depicts a square base pyramid. The dimensions given are:
- The length of each side of the square base is 27 mm.
- The slant height from the midpoint of one side of the square base to the apex of the pyramid is 35 mm.
**Detailed Steps to Solve for Surface Area:**
1. **Calculate the Base Area:**
The base of the pyramid is a square. The area of a square is calculated as:
\[
\text{Base Area} = \text{side length}^2 = 27 \times 27 = 729 \text{ mm}^2
\]
2. **Calculate the Lateral Surface Area:**
The lateral surface area consists of four triangular faces.
The area of one triangular face can be calculated using:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base of the triangle} \times \text{slant height}
\]
For the given pyramid,
\[
\text{Area of one triangle} = \frac{1}{2} \times 27 \times 35 = \frac{1}{2} \times 945 = 472.5 \text{ mm}^2
\]
Since there are four triangular faces,
\[
\text{Total Lateral Surface Area} = 4 \times 472.5 = 1890 \text{ mm}^2
\]
3. **Calculate the Total Surface Area:**
The total surface area of the pyramid is the sum of the base area and the lateral surface area:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Surface Area} = 729 + 1890 = 2619 \text{ mm}^2
\]
**Final Answer:**
The surface area of the square base pyramid is \(2619 \text{ mm}^2\).
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