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
Find the area of the decagon
![### Educational Content
#### Geometry Problems
**8. Find the measure of the central angle of a regular polygon with 16 sides.**
Given:
- Number of sides (n) = 16
The measure of the central angle of a regular polygon can be calculated using the formula:
\[ \text{Central Angle} = \frac{360^\circ}{n} \]
Applying the formula:
\[ \text{Central Angle} = \frac{360^\circ}{16} = 22.5^\circ \]
**Note**: The provided answer in the image is `157.5`, which might be an error. The correct central angle is `22.5 degrees`.
**9. Find the area of the decagon. Round your answer to the nearest hundredth.**
Below the text, there is a diagram of a regular decagon (a 10-sided polygon). The decagon is labeled with an area symbol in one of its internal segments.
To calculate the area of a regular decagon (10-sided polygon), you can use the formula:
\[ \text{Area} = \frac{5}{2} \times a \times s \]
where:
- \( a \) is the apothem (the line from the center to the midpoint of one of its sides),
- \( s \) is the length of one side of the decagon.
If the length of one side is not given, the problem may require additional steps to determine it based on other provided information such as the radius or the apothem.
You can input the value into the text box provided below the diagram to round your answer to the nearest hundredth.
**Diagram Description:**
The diagram shows a regular decagon with an apothem drawn from the center to the midpoint of one side. The apothem is denoted by an 'a' along with a right angle symbol indicating it forms a right triangle with half of one of the sides and the line segment connecting the center to a vertex.
Please complete the solution with given or derived measurements. Once the necessary values (side length and apothem) are identified, substitute them into the above formula to calculate and round the area to the nearest hundredth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e9d242-cb37-4bc8-a74f-f7cca1efbc15%2Fd946609a-20d2-429f-8c28-d4f6991f9275%2Fqrg1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content
#### Geometry Problems
**8. Find the measure of the central angle of a regular polygon with 16 sides.**
Given:
- Number of sides (n) = 16
The measure of the central angle of a regular polygon can be calculated using the formula:
\[ \text{Central Angle} = \frac{360^\circ}{n} \]
Applying the formula:
\[ \text{Central Angle} = \frac{360^\circ}{16} = 22.5^\circ \]
**Note**: The provided answer in the image is `157.5`, which might be an error. The correct central angle is `22.5 degrees`.
**9. Find the area of the decagon. Round your answer to the nearest hundredth.**
Below the text, there is a diagram of a regular decagon (a 10-sided polygon). The decagon is labeled with an area symbol in one of its internal segments.
To calculate the area of a regular decagon (10-sided polygon), you can use the formula:
\[ \text{Area} = \frac{5}{2} \times a \times s \]
where:
- \( a \) is the apothem (the line from the center to the midpoint of one of its sides),
- \( s \) is the length of one side of the decagon.
If the length of one side is not given, the problem may require additional steps to determine it based on other provided information such as the radius or the apothem.
You can input the value into the text box provided below the diagram to round your answer to the nearest hundredth.
**Diagram Description:**
The diagram shows a regular decagon with an apothem drawn from the center to the midpoint of one side. The apothem is denoted by an 'a' along with a right angle symbol indicating it forms a right triangle with half of one of the sides and the line segment connecting the center to a vertex.
Please complete the solution with given or derived measurements. Once the necessary values (side length and apothem) are identified, substitute them into the above formula to calculate and round the area to the nearest hundredth.
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