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
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**Geometry Exercise: Finding the Area of a Regular Polygon**
**Question:**
Find the area of the regular polygon below:
[Diagram of a Pentagon]
- Side length = 5.5 meters
- Apothem = 8 meters
**Options:**
- A. 55 m²
- B. 110 m²
- C. 220 m² (Note: This option is crossed out)
- D. 44 m²
**Explanation of Diagram:**
The diagram depicts a regular pentagon with all sides equal in length. Each side of the pentagon measures 5.5 meters. The apothem, which is the perpendicular distance from the center to one of its sides, measures 8 meters.
**Solution Approach:**
To find the area \(A\) of a regular polygon, you can use the formula:
\[ A = \frac{1}{2} \times Perimeter \times Apothem \]
For a regular pentagon:
- The Perimeter \(P\) is calculated by multiplying the side length by the number of sides. Since the pentagon has 5 sides:
\[ P = 5 \times 5.5 \, \text{meters} \]
\[ P = 27.5 \, \text{meters} \]
- The Apothem provided is 8 meters.
Now, substitute these values into the area formula:
\[ A = \frac{1}{2} \times 27.5 \, \text{meters} \times 8 \, \text{meters} \]
\[ A = \frac{1}{2} \times 220 \, \text{m}^2 \]
\[ A = 110 \, \text{m}^2 \]
Therefore, the correct answer is:
- **B. 110 m²**
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Transcribed Image Text:---
**Geometry Exercise: Finding the Area of a Regular Polygon**
**Question:**
Find the area of the regular polygon below:
[Diagram of a Pentagon]
- Side length = 5.5 meters
- Apothem = 8 meters
**Options:**
- A. 55 m²
- B. 110 m²
- C. 220 m² (Note: This option is crossed out)
- D. 44 m²
**Explanation of Diagram:**
The diagram depicts a regular pentagon with all sides equal in length. Each side of the pentagon measures 5.5 meters. The apothem, which is the perpendicular distance from the center to one of its sides, measures 8 meters.
**Solution Approach:**
To find the area \(A\) of a regular polygon, you can use the formula:
\[ A = \frac{1}{2} \times Perimeter \times Apothem \]
For a regular pentagon:
- The Perimeter \(P\) is calculated by multiplying the side length by the number of sides. Since the pentagon has 5 sides:
\[ P = 5 \times 5.5 \, \text{meters} \]
\[ P = 27.5 \, \text{meters} \]
- The Apothem provided is 8 meters.
Now, substitute these values into the area formula:
\[ A = \frac{1}{2} \times 27.5 \, \text{meters} \times 8 \, \text{meters} \]
\[ A = \frac{1}{2} \times 220 \, \text{m}^2 \]
\[ A = 110 \, \text{m}^2 \]
Therefore, the correct answer is:
- **B. 110 m²**
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