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 16: Calculating the Area of a Regular Polygon**
**Problem Statement:**
Find the area of the regular polygon below:
(Here, there is a diagram of a regular pentagon with an apothem (perpendicular distance from the center to a side) of 5.5 meters and a side length of 8 meters.)
**Options:**
A. 55 m²
B. 110 m²
C. 220 m²
D. 44 m²
**Solution:**
To find the area of a regular polygon, the formula is:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]
1. **Calculate the perimeter of the pentagon:**
A regular pentagon has 5 sides. Given each side length is 8 m:
\[ \text{Perimeter} = 5 \times 8 = 40 \, \text{m} \]
2. **Insert the perimeter and apothem into the area formula:**
Given the apothem (a) is 5.5 m:
\[ \text{Area} = \frac{1}{2} \times 40 \, \text{m} \times 5.5 \, \text{m} \]
\[ \text{Area} = \frac{1}{2} \times 220 \, \text{m}^2 \]
\[ \text{Area} = 110 \, \text{m}^2 \]
Thus, the correct answer is:
B. 110 m²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4904ad93-6dcc-43fa-9122-8f69394907f2%2F6c6c12c3-9e33-4458-b88c-b281c4344a4e%2Fbunm5t7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 16: Calculating the Area of a Regular Polygon**
**Problem Statement:**
Find the area of the regular polygon below:
(Here, there is a diagram of a regular pentagon with an apothem (perpendicular distance from the center to a side) of 5.5 meters and a side length of 8 meters.)
**Options:**
A. 55 m²
B. 110 m²
C. 220 m²
D. 44 m²
**Solution:**
To find the area of a regular polygon, the formula is:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]
1. **Calculate the perimeter of the pentagon:**
A regular pentagon has 5 sides. Given each side length is 8 m:
\[ \text{Perimeter} = 5 \times 8 = 40 \, \text{m} \]
2. **Insert the perimeter and apothem into the area formula:**
Given the apothem (a) is 5.5 m:
\[ \text{Area} = \frac{1}{2} \times 40 \, \text{m} \times 5.5 \, \text{m} \]
\[ \text{Area} = \frac{1}{2} \times 220 \, \text{m}^2 \]
\[ \text{Area} = 110 \, \text{m}^2 \]
Thus, the correct answer is:
B. 110 m²
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