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
Help me please
The trapezoid has the following measurements:
- The top base is 7 units.
- The bottom base is 15 units.
- The height of the trapezoid is 9 units.
- There is a right angle at both the top left and bottom right corners of the height.
The formula for the area \( A \) of a trapezoid is:
\[ A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
Substitute the given values:
\[ A = \frac{1}{2} \times (7 + 15) \times 9 \]
#### Calculation:
To find the area, carry out the following steps:
1. Add the lengths of the two bases:
\[ 7 + 15 = 22 \]
2. Multiply the sum of the bases by the height:
\[ 22 \times 9 = 198 \]
3. Divide the result by 2:
\[ \frac{198}{2} = 99 \]
So, the area \( A \) is
\[ A = 99 \text{ units}^2 \]
#### Provided Solution Format:
**A =** `Blank 1` **units^2**
Please fill in the blank with your answer:
**Blank 1:** `99`
This explanation carefully follows each step of determining the area of a trapezoid, ensuring understanding for educational purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74ca1d37-d294-4f01-9907-950537ec9baa%2F5ca00e0d-3cb9-47cb-be35-fa8a1d41281a%2Fq38ntgh_processed.png&w=3840&q=75)
Transcribed Image Text:### Find the Area of the Following Figure
#### Problem Statement:
Find the area of the following figure:
The trapezoid has the following measurements:
- The top base is 7 units.
- The bottom base is 15 units.
- The height of the trapezoid is 9 units.
- There is a right angle at both the top left and bottom right corners of the height.
The formula for the area \( A \) of a trapezoid is:
\[ A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
Substitute the given values:
\[ A = \frac{1}{2} \times (7 + 15) \times 9 \]
#### Calculation:
To find the area, carry out the following steps:
1. Add the lengths of the two bases:
\[ 7 + 15 = 22 \]
2. Multiply the sum of the bases by the height:
\[ 22 \times 9 = 198 \]
3. Divide the result by 2:
\[ \frac{198}{2} = 99 \]
So, the area \( A \) is
\[ A = 99 \text{ units}^2 \]
#### Provided Solution Format:
**A =** `Blank 1` **units^2**
Please fill in the blank with your answer:
**Blank 1:** `99`
This explanation carefully follows each step of determining the area of a trapezoid, ensuring understanding for educational purposes.
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