The area of the regular hexagon is 10.4 in.2. What is the measure of the apothem, rounded to the nearest tenth of an inch? 2 in. 1.3 in. 1.7 in. 2.0 in. 3.4 in. O O
The area of the regular hexagon is 10.4 in.2. What is the measure of the apothem, rounded to the nearest tenth of an inch? 2 in. 1.3 in. 1.7 in. 2.0 in. 3.4 in. O O
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
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![### Regular Hexagon Area and Apothem Calculation
**Problem Statement:**
The area of a regular hexagon is 10.4 square inches. Given this information, determine the measure of the apothem, rounded to the nearest tenth of an inch.
**Diagram Explanation:**
The provided diagram shows a regular hexagon with the following:
- A side length of 2 inches.
- An apothem (a perpendicular line from the center to the midpoint of one of the sides).
- A right-angle indicator where the apothem meets the side of the hexagon.
**Question:**
What is the measure of the apothem, rounded to the nearest tenth of an inch?
**Multiple Choice Answers:**
- A. 1.3 in.
- B. 1.7 in.
- C. 2.0 in.
- D. 3.4 in.
### Solution:
To find the apothem of a regular hexagon when the area is known, we use the formula for the area of a regular hexagon:
\[ \text{Area} = \frac{3\sqrt{3}}{2} \times \text{side length}^2 \]
However, a more direct approach considering the area and the apothem involves another formula:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]
Given:
- Area = 10.4 square inches
- Perimeter = 6 \times \text{side length} = 6 \times 2 = 12 inches
Rearranging the formula to solve for the apothem:
\[ \text{Apothem} = \frac{2 \times \text{Area}}{\text{Perimeter}} \]
\[ \text{Apothem} = \frac{2 \times 10.4}{12} \]
\[ \text{Apothem} \approx 1.733 \text{ inches} \]
Rounding to the nearest tenth:
\[ \text{Apothem} \approx 1.7 \text{ inches} \]
**Correct Answer:**
- B. 1.7 in.
### Submission Guidance
After calculating the apothem to be 1.7 inches, you can select the appropriate answer choice and proceed with the submission. Make sure to save your](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2F4d6c2891-e1f8-471e-8e7f-7882231e23a3%2Fmo4bhfp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Regular Hexagon Area and Apothem Calculation
**Problem Statement:**
The area of a regular hexagon is 10.4 square inches. Given this information, determine the measure of the apothem, rounded to the nearest tenth of an inch.
**Diagram Explanation:**
The provided diagram shows a regular hexagon with the following:
- A side length of 2 inches.
- An apothem (a perpendicular line from the center to the midpoint of one of the sides).
- A right-angle indicator where the apothem meets the side of the hexagon.
**Question:**
What is the measure of the apothem, rounded to the nearest tenth of an inch?
**Multiple Choice Answers:**
- A. 1.3 in.
- B. 1.7 in.
- C. 2.0 in.
- D. 3.4 in.
### Solution:
To find the apothem of a regular hexagon when the area is known, we use the formula for the area of a regular hexagon:
\[ \text{Area} = \frac{3\sqrt{3}}{2} \times \text{side length}^2 \]
However, a more direct approach considering the area and the apothem involves another formula:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]
Given:
- Area = 10.4 square inches
- Perimeter = 6 \times \text{side length} = 6 \times 2 = 12 inches
Rearranging the formula to solve for the apothem:
\[ \text{Apothem} = \frac{2 \times \text{Area}}{\text{Perimeter}} \]
\[ \text{Apothem} = \frac{2 \times 10.4}{12} \]
\[ \text{Apothem} \approx 1.733 \text{ inches} \]
Rounding to the nearest tenth:
\[ \text{Apothem} \approx 1.7 \text{ inches} \]
**Correct Answer:**
- B. 1.7 in.
### Submission Guidance
After calculating the apothem to be 1.7 inches, you can select the appropriate answer choice and proceed with the submission. Make sure to save your
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