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 trapezoid.
![**Calculating the Area of a Trapezoid**
To find the area of a trapezoid, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
where:
- \( b_1 \) is the length of the first base
- \( b_2 \) is the length of the second base
- \( h \) is the height of the trapezoid
**Problem**
Find the area of the following trapezoid.
The trapezoid has the following dimensions:
- The length of the top base, \( b_1 \), is 9 units.
- The length of the bottom base, \( b_2 \), is 15 units.
- The height, \( h \), is 15 units.
- An additional length in the diagram shows 18 units directly above the height, but it does not affect the final calculations for the area.
**Diagram Explanation**
- The trapezoid is depicted with a right angle indicating the height of 15 units.
- The top base is labeled as 9 units.
- The bottom base is labeled as 15 units.
- An internal segment (above the height) is labeled as 18 units, however, it is not needed for the area calculation.
**Solution**
Using the area formula for a trapezoid:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
\[ \text{Area} = \frac{1}{2} \times (9 + 15) \times 15 \]
\[ \text{Area} = \frac{1}{2} \times 24 \times 15 \]
\[ \text{Area} = 12 \times 15 \]
\[ \text{Area} = 180 \]
The area of the trapezoid is 180 square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdabcb075-25d2-4740-a604-c21c32053491%2F28fee7a6-7663-4d8f-8027-8a1b7e9d5cd8%2F9dstiu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Area of a Trapezoid**
To find the area of a trapezoid, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
where:
- \( b_1 \) is the length of the first base
- \( b_2 \) is the length of the second base
- \( h \) is the height of the trapezoid
**Problem**
Find the area of the following trapezoid.
The trapezoid has the following dimensions:
- The length of the top base, \( b_1 \), is 9 units.
- The length of the bottom base, \( b_2 \), is 15 units.
- The height, \( h \), is 15 units.
- An additional length in the diagram shows 18 units directly above the height, but it does not affect the final calculations for the area.
**Diagram Explanation**
- The trapezoid is depicted with a right angle indicating the height of 15 units.
- The top base is labeled as 9 units.
- The bottom base is labeled as 15 units.
- An internal segment (above the height) is labeled as 18 units, however, it is not needed for the area calculation.
**Solution**
Using the area formula for a trapezoid:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
\[ \text{Area} = \frac{1}{2} \times (9 + 15) \times 15 \]
\[ \text{Area} = \frac{1}{2} \times 24 \times 15 \]
\[ \text{Area} = 12 \times 15 \]
\[ \text{Area} = 180 \]
The area of the trapezoid is 180 square units.
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