Find the surface area of the following figure. Round your answer to the nearest tenth. 14.2 m 11 m 11 m
Find the surface area of the following figure. Round your answer to the nearest tenth. 14.2 m 11 m 11 m
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem Statement:**
Find the surface area of the following figure. Round your answer to the nearest tenth.
**Diagram:**
The diagram shows a pyramid with a square base. The label for the edges of the base shows each side to be 11 meters. Four triangular faces extend from the base to a common vertex. Each slant height of the triangular face is labeled as 14.2 meters.
### Explanation:
Given a pyramid with a square base where each side of the base is 11 meters and the slant height of each of the triangular faces is 14.2 meters, we need to calculate the surface area.
### Steps to Calculate Surface Area:
1. **Calculate the area of the base:**
The base is a square.
\[
\text{Area of the base} = \text{side}^2 = 11 \times 11 = 121 \, \text{m}^2
\]
2. **Calculate the area of one triangular face:**
The formula for the area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\).
Here, the base of the triangle is a side of the square base of the pyramid, which is 11 meters, and the height is the slant height, which is 14.2 meters.
\[
\text{Area of one triangular face} = \frac{1}{2} \times 11 \times 14.2 = \frac{1}{2} \times 156.2 = 78.1 \, \text{m}^2
\]
3. **Calculate the total area of the four triangular faces:**
\[
\text{Total area of the four triangular faces} = 4 \times 78.1 = 312.4 \, \text{m}^2
\]
4. **Calculate the surface area of the pyramid:**
\[
\text{Surface area} = \text{Area of the base} + \text{Total area of the triangular faces} = 121 + 312.4 = 433.4 \, \text{m}^2
\]
### Answer:
The surface area of the pyramid, rounded to the nearest tenth, is **433.4 square meters**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90d845b0-37dd-4edd-a406-0af795a71ce1%2F71439076-7958-4b3d-8302-c01e242b294d%2Ftmsu6wt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the surface area of the following figure. Round your answer to the nearest tenth.
**Diagram:**
The diagram shows a pyramid with a square base. The label for the edges of the base shows each side to be 11 meters. Four triangular faces extend from the base to a common vertex. Each slant height of the triangular face is labeled as 14.2 meters.
### Explanation:
Given a pyramid with a square base where each side of the base is 11 meters and the slant height of each of the triangular faces is 14.2 meters, we need to calculate the surface area.
### Steps to Calculate Surface Area:
1. **Calculate the area of the base:**
The base is a square.
\[
\text{Area of the base} = \text{side}^2 = 11 \times 11 = 121 \, \text{m}^2
\]
2. **Calculate the area of one triangular face:**
The formula for the area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\).
Here, the base of the triangle is a side of the square base of the pyramid, which is 11 meters, and the height is the slant height, which is 14.2 meters.
\[
\text{Area of one triangular face} = \frac{1}{2} \times 11 \times 14.2 = \frac{1}{2} \times 156.2 = 78.1 \, \text{m}^2
\]
3. **Calculate the total area of the four triangular faces:**
\[
\text{Total area of the four triangular faces} = 4 \times 78.1 = 312.4 \, \text{m}^2
\]
4. **Calculate the surface area of the pyramid:**
\[
\text{Surface area} = \text{Area of the base} + \text{Total area of the triangular faces} = 121 + 312.4 = 433.4 \, \text{m}^2
\]
### Answer:
The surface area of the pyramid, rounded to the nearest tenth, is **433.4 square meters**.
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