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
![**Problem:**
Find the area of the regular octagon ABCDEFGH. The apothem measures 10 cm. Segment GH measures about 8.3 cm.
**Solution:**
To determine the area of the regular octagon, we can use the formula for the area of a regular polygon:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]
First, let's find the perimeter (P) of the octagon.
Each side (s) of the regular octagon can be calculated knowing that:
- Segment GH is one of the sides.
- The regular octagon has 8 equal sides.
Given segment GH = 8.3 cm:
\[ P = 8 \times s = 8 \times 8.3\, \text{cm} = 66.4\, \text{cm} \]
Now, we use the apothem (a) given as 10 cm.
\[ \text{Area} = \frac{1}{2} \times 66.4 \, \text{cm} \times 10 \, \text{cm} \]
\[ \text{Area} = \frac{1}{2} \times 664 \, \text{cm}^2 \]
\[ \text{Area} = 332 \, \text{cm}^2 \]
Thus, the area of the regular octagon ABCDEFGH is **332 square centimeters**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccc6c07f-901f-4b9b-9990-bf05e0ed87d5%2Fcaac451b-74d4-4466-8793-6f309ddf19c3%2Fgx21gbj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the area of the regular octagon ABCDEFGH. The apothem measures 10 cm. Segment GH measures about 8.3 cm.
**Solution:**
To determine the area of the regular octagon, we can use the formula for the area of a regular polygon:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \]
First, let's find the perimeter (P) of the octagon.
Each side (s) of the regular octagon can be calculated knowing that:
- Segment GH is one of the sides.
- The regular octagon has 8 equal sides.
Given segment GH = 8.3 cm:
\[ P = 8 \times s = 8 \times 8.3\, \text{cm} = 66.4\, \text{cm} \]
Now, we use the apothem (a) given as 10 cm.
\[ \text{Area} = \frac{1}{2} \times 66.4 \, \text{cm} \times 10 \, \text{cm} \]
\[ \text{Area} = \frac{1}{2} \times 664 \, \text{cm}^2 \]
\[ \text{Area} = 332 \, \text{cm}^2 \]
Thus, the area of the regular octagon ABCDEFGH is **332 square centimeters**.
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