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
![### Diagram Explanation:
The image depicts a geometric shape divided into two distinct regions labeled A and B.
- **Region A**:
- This area forms a rectangle.
- Dimensions are provided: width is 6 feet, height is 9 feet.
- **Region B**:
- This area forms a triangle directly below the rectangle.
- The base of the triangle aligns with the width of the rectangle, measuring 6 feet.
### Additional Measurements:
- The total height of the combined shape (rectangle and triangle) is 14 feet.
### Area Calculation:
The area for the given shape is left to be calculated at the bottom of the image, shown as:
- **Area =** (without any numerical value filled in).
### Notes:
- The area of Region A (the rectangle) can be calculated using the formula:
\[ \text{Area of A} = \text{width} \times \text{height} = 6\,\text{ft} \times 9\,\text{ft} \]
- The area of Region B (the triangle) can be calculated using the formula:
\[ \text{Area of B} = \frac{1}{2} \times \text{base} \times \text{height} \]
- To determine the height of the triangle, subtract the height of the rectangle from the total height: \( 14\,\text{ft} - 9\,\text{ft} = 5\,\text{ft} \).
### Provided Area Information:
- There is an additional unrelated area value noted at the top left of the image:
\[ \text{Area} = 34\,\text{yd} \]
This information can serve as a practical problem case for calculating combined shapes and understanding basic geometric property evaluations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa845f802-60f3-4c15-8425-576c0ee51580%2Fac13765a-970f-451d-97c5-ab4b4442a839%2Fc286e15_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Diagram Explanation:
The image depicts a geometric shape divided into two distinct regions labeled A and B.
- **Region A**:
- This area forms a rectangle.
- Dimensions are provided: width is 6 feet, height is 9 feet.
- **Region B**:
- This area forms a triangle directly below the rectangle.
- The base of the triangle aligns with the width of the rectangle, measuring 6 feet.
### Additional Measurements:
- The total height of the combined shape (rectangle and triangle) is 14 feet.
### Area Calculation:
The area for the given shape is left to be calculated at the bottom of the image, shown as:
- **Area =** (without any numerical value filled in).
### Notes:
- The area of Region A (the rectangle) can be calculated using the formula:
\[ \text{Area of A} = \text{width} \times \text{height} = 6\,\text{ft} \times 9\,\text{ft} \]
- The area of Region B (the triangle) can be calculated using the formula:
\[ \text{Area of B} = \frac{1}{2} \times \text{base} \times \text{height} \]
- To determine the height of the triangle, subtract the height of the rectangle from the total height: \( 14\,\text{ft} - 9\,\text{ft} = 5\,\text{ft} \).
### Provided Area Information:
- There is an additional unrelated area value noted at the top left of the image:
\[ \text{Area} = 34\,\text{yd} \]
This information can serve as a practical problem case for calculating combined shapes and understanding basic geometric property evaluations.
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