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
Mrs smith asked the class to find the area of this figure. What answer should the students come up with?
![**Geometry Lesson: Problem Solving with Trapezoids**
**Topic: Calculating Area of a Trapezoid**
**Problem Statement:**
Mrs. Smith asked the class to solve a geometry problem involving the area of a trapezoid. The question posed was:
**"What is the area of the trapezoid Mrs. Smith asked the class to come up with?"**
**Diagram Description:**
The diagram provided illustrates a trapezoid with the following dimensions:
- The height of the trapezoid is represented by two vertical lines labeled 5 units each, indicating sections of height that are consistent across the trapezoid's vertical dimension.
- The two parallel sides (bases) of the trapezoid are labeled as follows:
- The shorter base (top) is labeled 8 units.
- The longer base (bottom) is labeled 14 units.
**Formula for the Area of a Trapezoid:**
To find the area of a trapezoid, use the following formula:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
where \(\text{Base}_1\) and \(\text{Base}_2\) are the lengths of the two parallel sides, and \(\text{Height}\) is the perpendicular distance between these bases.
**Solution:**
Substitute the given values into the formula:
\[ \text{Area} = \frac{1}{2} \times (8 \, \text{units} + 14 \, \text{units}) \times 5 \, \text{units} \]
\[ \text{Area} = \frac{1}{2} \times 22 \, \text{units} \times 5 \, \text{units} \]
\[ \text{Area} = \frac{1}{2} \times 110 \, \text{square units} \]
\[ \text{Area} = 55 \, \text{square units} \]
Therefore, the area of the trapezoid is 55 square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F870e2c1d-d022-4f41-b5d2-13ea4c5e7ced%2Fee43ef80-945f-4e70-a43a-f24e4cfc6e19%2Fq99ggh4.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Lesson: Problem Solving with Trapezoids**
**Topic: Calculating Area of a Trapezoid**
**Problem Statement:**
Mrs. Smith asked the class to solve a geometry problem involving the area of a trapezoid. The question posed was:
**"What is the area of the trapezoid Mrs. Smith asked the class to come up with?"**
**Diagram Description:**
The diagram provided illustrates a trapezoid with the following dimensions:
- The height of the trapezoid is represented by two vertical lines labeled 5 units each, indicating sections of height that are consistent across the trapezoid's vertical dimension.
- The two parallel sides (bases) of the trapezoid are labeled as follows:
- The shorter base (top) is labeled 8 units.
- The longer base (bottom) is labeled 14 units.
**Formula for the Area of a Trapezoid:**
To find the area of a trapezoid, use the following formula:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
where \(\text{Base}_1\) and \(\text{Base}_2\) are the lengths of the two parallel sides, and \(\text{Height}\) is the perpendicular distance between these bases.
**Solution:**
Substitute the given values into the formula:
\[ \text{Area} = \frac{1}{2} \times (8 \, \text{units} + 14 \, \text{units}) \times 5 \, \text{units} \]
\[ \text{Area} = \frac{1}{2} \times 22 \, \text{units} \times 5 \, \text{units} \]
\[ \text{Area} = \frac{1}{2} \times 110 \, \text{square units} \]
\[ \text{Area} = 55 \, \text{square units} \]
Therefore, the area of the trapezoid is 55 square units.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
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