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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![**Title: Calculating the Perimeter and Area of an Irregular Figure**
**Description:**
In this tutorial, we will learn how to find both the perimeter and the area of an L-shaped figure.
**Figure:**
The figure shown is an L-shaped polygon with the following dimensions:
- The vertical segment on the left measures 11.9 meters.
- The segment extending horizontally from the bottom left to the interior corner measures 12 meters.
- The vertical segment extending from the interior corner upwards measures 3 meters.
- The horizontal top segment of the L shape measures 4.1 meters.
**Step-by-Step Breakdown:**
**1. Perimeter Calculation:**
To calculate the perimeter, add the lengths of all the outer sides of the figure.
**Formula:**
\[ \text{Perimeter} = 11.9 \, \text{m} + 12 \, \text{m} + 4.1 \, \text{m} + (\text{remaining horizontal segment}) + (\text{remaining vertical segment}) \]
Note: The remaining horizontal and vertical segments can be found from the total subtracting the dimensions given.
For the vertical segments:
\[ \text{Total height} = 11.9 \, \text{m} \]
\[ \text{Top segment} + \text{bottom vertical segment} = 11.9 \, \text{m} \]
\[ \text{Bottom vertical} = 11.9 \, \text{m} - 3 \, \text{m} \]
For the horizontal segments:
\[ \text{Total width} = 12 \, \text{m} \]
\[ \text{Left side segment} + \text{right side segment} = 12 \, \text{m} \]
\[ \text{Right side segment} = 12 \, \text{m} - 4.1 \, \text{m} \]
\[ \text{Perimeter} = 11.9 \, \text{m} + 12 \, \text{m} + 4.1 \, \text{m} + (12 - 4.1) \, \text{m} + (11.9 - 3) \, \text{m} \]
\[ \text{Perimeter} = 11.9 \, \text{m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa75e9829-b392-4f4d-a17a-dd8f5cc30db1%2F84a399ea-b9d0-4bc3-b47b-96f3906fa310%2Fnvrhr5u.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Perimeter and Area of an Irregular Figure**
**Description:**
In this tutorial, we will learn how to find both the perimeter and the area of an L-shaped figure.
**Figure:**
The figure shown is an L-shaped polygon with the following dimensions:
- The vertical segment on the left measures 11.9 meters.
- The segment extending horizontally from the bottom left to the interior corner measures 12 meters.
- The vertical segment extending from the interior corner upwards measures 3 meters.
- The horizontal top segment of the L shape measures 4.1 meters.
**Step-by-Step Breakdown:**
**1. Perimeter Calculation:**
To calculate the perimeter, add the lengths of all the outer sides of the figure.
**Formula:**
\[ \text{Perimeter} = 11.9 \, \text{m} + 12 \, \text{m} + 4.1 \, \text{m} + (\text{remaining horizontal segment}) + (\text{remaining vertical segment}) \]
Note: The remaining horizontal and vertical segments can be found from the total subtracting the dimensions given.
For the vertical segments:
\[ \text{Total height} = 11.9 \, \text{m} \]
\[ \text{Top segment} + \text{bottom vertical segment} = 11.9 \, \text{m} \]
\[ \text{Bottom vertical} = 11.9 \, \text{m} - 3 \, \text{m} \]
For the horizontal segments:
\[ \text{Total width} = 12 \, \text{m} \]
\[ \text{Left side segment} + \text{right side segment} = 12 \, \text{m} \]
\[ \text{Right side segment} = 12 \, \text{m} - 4.1 \, \text{m} \]
\[ \text{Perimeter} = 11.9 \, \text{m} + 12 \, \text{m} + 4.1 \, \text{m} + (12 - 4.1) \, \text{m} + (11.9 - 3) \, \text{m} \]
\[ \text{Perimeter} = 11.9 \, \text{m
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