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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**Finding the Perimeter of a Polygon**
To determine the perimeter of the polygon presented in the image, follow these steps:
1. **Identify the Sides**:
- The polygon in the image is a triangle labeled ABC.
- The lengths of the sides are marked as:
- AB = 22
- BC = 9
- AC = 12
2. **Calculate the Perimeter**:
- The perimeter of a polygon is the sum of the lengths of all its sides.
- Thus, in our case, for the triangle ABC:
\[ \text{Perimeter} = AB + BC + AC \]
\[ \text{Perimeter} = 22 + 9 + 12 \]
\[ \text{Perimeter} = 43 \]
3. **Conclusion**:
- The perimeter of the given triangle ABC is 43 units.
**Detailed Explanation of the Diagram**:
The diagram represents a triangle ABC with the following characteristics:
- Points E, F, and D are points of tangency of the incircle with the sides of the triangle.
- An incircle (a circle inscribed within the triangle) is tangent to the sides at points E, F, and D.
- The vertices of the triangle are denoted as A, B, and C.
- The lengths of the sides AB, BC, and AC are given as 22, 9, and 12 units respectively.
This detailed breakdown should assist learners in understanding how to calculate the perimeter of a triangle using given side lengths.
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Transcribed Image Text:---
**Finding the Perimeter of a Polygon**
To determine the perimeter of the polygon presented in the image, follow these steps:
1. **Identify the Sides**:
- The polygon in the image is a triangle labeled ABC.
- The lengths of the sides are marked as:
- AB = 22
- BC = 9
- AC = 12
2. **Calculate the Perimeter**:
- The perimeter of a polygon is the sum of the lengths of all its sides.
- Thus, in our case, for the triangle ABC:
\[ \text{Perimeter} = AB + BC + AC \]
\[ \text{Perimeter} = 22 + 9 + 12 \]
\[ \text{Perimeter} = 43 \]
3. **Conclusion**:
- The perimeter of the given triangle ABC is 43 units.
**Detailed Explanation of the Diagram**:
The diagram represents a triangle ABC with the following characteristics:
- Points E, F, and D are points of tangency of the incircle with the sides of the triangle.
- An incircle (a circle inscribed within the triangle) is tangent to the sides at points E, F, and D.
- The vertices of the triangle are denoted as A, B, and C.
- The lengths of the sides AB, BC, and AC are given as 22, 9, and 12 units respectively.
This detailed breakdown should assist learners in understanding how to calculate the perimeter of a triangle using given side lengths.
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