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
![### Question:
A regular hexagon has a radius of 20 in. What is the approximate area of the hexagon?
1. 600 in²
2. 1,038 in²
3. 1,200 in²
4. 2,076 in²
### Answer Options:
- **600 in²**
- **1,038 in²**
- **1,200 in²**
- **2,076 in²**
### Actions:
- **Mark this and return**
- **Save and Exit**
- **Next**
- **Submit**
### Explanation:
This question is presented in a multiple-choice format, where the user is asked to determine the area of a regular hexagon, given a radius of 20 inches. The possible answers are displayed as four different numerical values with the unit in square inches (in²).
To solve this problem, students should be familiar with the formula for the area of a regular hexagon. The formula for the area (A) of a regular hexagon with a given radius (r) is:
\[ A = \frac{3 \sqrt{3}}{2} \times r^2 \]
Substituting \( r = 20 \) into the formula:
\[ A = \frac{3 \sqrt{3}}{2} \times (20)^2 \]
\[ A \approx \frac{3 \times 1.732}{2} \times 400 \]
\[ A \approx \frac{5.196}{2} \times 400 \]
\[ A \approx 2.598 \times 400 \]
\[ A \approx 1039.2 \text{ in}^2 \]
Thus, the closest answer is 1,038 in².
Selecting the correct value from the provided options verifies the understanding of calculating the area of a geometric shape using its radius. The interface allows the student to save their progress, continue to the next question, or submit their answer immediately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2F9d5c2df1-e50d-43e3-bae6-0fa14bdf439d%2Fcwu3mlm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question:
A regular hexagon has a radius of 20 in. What is the approximate area of the hexagon?
1. 600 in²
2. 1,038 in²
3. 1,200 in²
4. 2,076 in²
### Answer Options:
- **600 in²**
- **1,038 in²**
- **1,200 in²**
- **2,076 in²**
### Actions:
- **Mark this and return**
- **Save and Exit**
- **Next**
- **Submit**
### Explanation:
This question is presented in a multiple-choice format, where the user is asked to determine the area of a regular hexagon, given a radius of 20 inches. The possible answers are displayed as four different numerical values with the unit in square inches (in²).
To solve this problem, students should be familiar with the formula for the area of a regular hexagon. The formula for the area (A) of a regular hexagon with a given radius (r) is:
\[ A = \frac{3 \sqrt{3}}{2} \times r^2 \]
Substituting \( r = 20 \) into the formula:
\[ A = \frac{3 \sqrt{3}}{2} \times (20)^2 \]
\[ A \approx \frac{3 \times 1.732}{2} \times 400 \]
\[ A \approx \frac{5.196}{2} \times 400 \]
\[ A \approx 2.598 \times 400 \]
\[ A \approx 1039.2 \text{ in}^2 \]
Thus, the closest answer is 1,038 in².
Selecting the correct value from the provided options verifies the understanding of calculating the area of a geometric shape using its radius. The interface allows the student to save their progress, continue to the next question, or submit their answer immediately.
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