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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Question
![**Geometry Exercise: Perimeter of a Quadrilateral**
**Problem Statement:**
What is the perimeter of quadrilateral \(MNPQ\)?
**Given Data:**
- Triangle \(MNQ\) is formed with \(MN = 6\), \(NP = 3\), and two angles \(\angle MQN = 60^\circ\) and \(\angle PQM = 60^\circ\).
**Task:**
Calculate the perimeter of quadrilateral \(MNPQ\).
**Diagram Description:**
- The provided diagram shows points \(M, N, P,\) and \(Q\) forming quadrilateral \(MNPQ\).
- \(MN\) is 6 units.
- \(NP\) is 3 units.
- Both \(\angle MQN\) and \(\angle PQM\) are \(60^\circ\).
**Solution Steps:**
To find the perimeter of quadrilateral \(MNPQ\), you need to sum the lengths of all its sides:
\[ \text{Perimeter of } MNPQ = MN + NP + PQ + QM \]
Use the given lengths and calculated lengths from the diagram to find the total perimeter.
**Calculation:**
1. Identify and mark the lengths of all sides.
2. Use trigonometric relationships or geometry principles if necessary to find any unknown side lengths.
3. Sum all side lengths.
\[ \text{Perimeter of } MNPQ = 6 + 3 + PQ + QM \]
Find \(PQ\) and \(QM\) if not directly given in the problem.
**Answer Box:**
\[ \text{Perimeter of } MNPQ = \]
(Ensure to solve for all sides before submitting the final answer.)
**Note:**
To calculate the exact perimeter, one may need additional details not provided in the above description such as length of sides \(PQ\) and \(QM\) if they are not directly deduced from the given information. Use geometric properties and relationships among angles and sides for complete solution.
**Submit your Answer:**
Click the box to enter your final perimeter calculation and submit.
**Educational Value:**
This exercise helps in understanding the application of geometric principles, trigonometric relationships, and the computation of perimeters in polygons.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61108dbe-6367-4cda-8da7-cf2dec870a3d%2Fe13ad25f-14b8-4ff6-a2e2-5fd74ab690ea%2F992mzl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Exercise: Perimeter of a Quadrilateral**
**Problem Statement:**
What is the perimeter of quadrilateral \(MNPQ\)?
**Given Data:**
- Triangle \(MNQ\) is formed with \(MN = 6\), \(NP = 3\), and two angles \(\angle MQN = 60^\circ\) and \(\angle PQM = 60^\circ\).
**Task:**
Calculate the perimeter of quadrilateral \(MNPQ\).
**Diagram Description:**
- The provided diagram shows points \(M, N, P,\) and \(Q\) forming quadrilateral \(MNPQ\).
- \(MN\) is 6 units.
- \(NP\) is 3 units.
- Both \(\angle MQN\) and \(\angle PQM\) are \(60^\circ\).
**Solution Steps:**
To find the perimeter of quadrilateral \(MNPQ\), you need to sum the lengths of all its sides:
\[ \text{Perimeter of } MNPQ = MN + NP + PQ + QM \]
Use the given lengths and calculated lengths from the diagram to find the total perimeter.
**Calculation:**
1. Identify and mark the lengths of all sides.
2. Use trigonometric relationships or geometry principles if necessary to find any unknown side lengths.
3. Sum all side lengths.
\[ \text{Perimeter of } MNPQ = 6 + 3 + PQ + QM \]
Find \(PQ\) and \(QM\) if not directly given in the problem.
**Answer Box:**
\[ \text{Perimeter of } MNPQ = \]
(Ensure to solve for all sides before submitting the final answer.)
**Note:**
To calculate the exact perimeter, one may need additional details not provided in the above description such as length of sides \(PQ\) and \(QM\) if they are not directly deduced from the given information. Use geometric properties and relationships among angles and sides for complete solution.
**Submit your Answer:**
Click the box to enter your final perimeter calculation and submit.
**Educational Value:**
This exercise helps in understanding the application of geometric principles, trigonometric relationships, and the computation of perimeters in polygons.
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