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 following trapezoids:
![### Finding the Area of Trapezoids
To find the area of a trapezoid, use the formula:
\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]
where \(a\) and \(b\) are the lengths of the bases, and \(h\) is the height.
Below are three trapezoids for which you are asked to find the area.
#### Problem 7:
- **Bases**: \(14\) and \(10.6\)
- **Height**: The problem does not directly provide the height, and it uses two 70-degree angles and vertical lines to depict a possibly different scenario of calculation. However, under typical conditions using height would apply.
#### Problem 8:
- **Bases**: \(3\) and \(5\)
- **Height**: \(4\)
#### Problem 9:
- **Bases**: \(5\) and \(7\)
- **Height**: \(10\)
### Detailed Steps:
#### Problem 7:
This is a more complex trapezoid because it includes additional angle and side annotations. To find the height:
1. Understand the structure and the given dimensions effectively.
2. Use geometric properties or trigonometric ratios to determine the height, which requires considering given degrees.
#### Problem 8:
1. Add the bases: \(3 + 5 = 8\).
2. Multiply by the height: \(8 \times 4 = 32\).
3. Divide by 2: \( \frac{32}{2} = 16 \).
So, the area of trapezoid 8 is \( 16 \text{ square units} \).
#### Problem 9:
1. Add the bases: \(5 + 7 = 12\).
2. Multiply by the height: \(12 \times 10 = 120\).
3. Divide by 2: \( \frac{120}{2} = 60 \).
So, the area of trapezoid 9 is \( 60 \text{ square units} \).
Use these principles and calculations to find the area of each trapezoid. Practice helps in refining the understanding and application of these geometric concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9bce8c0-069b-44af-bdf7-a7daf1a8c7d3%2Fe108718e-8608-4493-8655-e1eafbfcba47%2F0dat9m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Area of Trapezoids
To find the area of a trapezoid, use the formula:
\[ \text{Area} = \frac{1}{2} \times (a + b) \times h \]
where \(a\) and \(b\) are the lengths of the bases, and \(h\) is the height.
Below are three trapezoids for which you are asked to find the area.
#### Problem 7:
- **Bases**: \(14\) and \(10.6\)
- **Height**: The problem does not directly provide the height, and it uses two 70-degree angles and vertical lines to depict a possibly different scenario of calculation. However, under typical conditions using height would apply.
#### Problem 8:
- **Bases**: \(3\) and \(5\)
- **Height**: \(4\)
#### Problem 9:
- **Bases**: \(5\) and \(7\)
- **Height**: \(10\)
### Detailed Steps:
#### Problem 7:
This is a more complex trapezoid because it includes additional angle and side annotations. To find the height:
1. Understand the structure and the given dimensions effectively.
2. Use geometric properties or trigonometric ratios to determine the height, which requires considering given degrees.
#### Problem 8:
1. Add the bases: \(3 + 5 = 8\).
2. Multiply by the height: \(8 \times 4 = 32\).
3. Divide by 2: \( \frac{32}{2} = 16 \).
So, the area of trapezoid 8 is \( 16 \text{ square units} \).
#### Problem 9:
1. Add the bases: \(5 + 7 = 12\).
2. Multiply by the height: \(12 \times 10 = 120\).
3. Divide by 2: \( \frac{120}{2} = 60 \).
So, the area of trapezoid 9 is \( 60 \text{ square units} \).
Use these principles and calculations to find the area of each trapezoid. Practice helps in refining the understanding and application of these geometric concepts.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning