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
![### Geometry Problem
#### Question 10
**Problem Statement:**
What is the area of this shape?
(Shape is displayed with specific measurements.)
**Dimensions of the Shape:**
- The combined shape consists of a rectangle and a semicircle on top of it.
- Height of the rectangle: 3 cm
- Width of the rectangle: 2 cm
- Radius of the semicircle: 2 cm (as it shares the same width as the rectangle)
- Height of the full shape (inclusive of the semicircle): 6 cm
**Diagram Details:**
The diagram shows a vertical rectangle with a semicircle on top of it. The rectangle is 3 cm tall and 2 cm wide. The semicircle, sitting on top of the rectangle, has a radius of 2 cm.
**Answer Options:**
A. 83.52 cm²
B. 55.26 cm²
C. 64.26 cm²
D. 36 cm²
---
### Detailed Analysis:
To solve this problem, we need to calculate the area of the rectangle and add it to the area of the semicircle.
1. **Area of the Rectangle:**
\[ \text{Area of Rectangle} = \text{width} \times \text{height} \]
\[ \text{Area of Rectangle} = 2 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2 \]
2. **Area of the Semicircle:**
- The formula for the area of a circle is \( \pi r^2 \), and since it’s a semicircle:
\[ \text{Area of Semicircle} = \frac{1}{2} \pi r^2 \]
\[ \text{Area of Semicircle} = \frac{1}{2} \pi (2 \, \text{cm})^2 = \frac{1}{2} \pi (4) \]
\[ \text{Area of Semicircle} = 2 \pi \, \text{cm}^2 \approx 6.28 \, \text{cm}^2 \]
3. **Total Area of the Shape:**
\[ \text{Total Area} = \text{Area of Rectangle} + \text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b4ac02d-8fa9-4cd1-ad8a-49ffeef4197d%2Ffe9ec05d-7970-4f06-b25f-8a9efd33cac9%2Ftr6jm2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem
#### Question 10
**Problem Statement:**
What is the area of this shape?
(Shape is displayed with specific measurements.)
**Dimensions of the Shape:**
- The combined shape consists of a rectangle and a semicircle on top of it.
- Height of the rectangle: 3 cm
- Width of the rectangle: 2 cm
- Radius of the semicircle: 2 cm (as it shares the same width as the rectangle)
- Height of the full shape (inclusive of the semicircle): 6 cm
**Diagram Details:**
The diagram shows a vertical rectangle with a semicircle on top of it. The rectangle is 3 cm tall and 2 cm wide. The semicircle, sitting on top of the rectangle, has a radius of 2 cm.
**Answer Options:**
A. 83.52 cm²
B. 55.26 cm²
C. 64.26 cm²
D. 36 cm²
---
### Detailed Analysis:
To solve this problem, we need to calculate the area of the rectangle and add it to the area of the semicircle.
1. **Area of the Rectangle:**
\[ \text{Area of Rectangle} = \text{width} \times \text{height} \]
\[ \text{Area of Rectangle} = 2 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2 \]
2. **Area of the Semicircle:**
- The formula for the area of a circle is \( \pi r^2 \), and since it’s a semicircle:
\[ \text{Area of Semicircle} = \frac{1}{2} \pi r^2 \]
\[ \text{Area of Semicircle} = \frac{1}{2} \pi (2 \, \text{cm})^2 = \frac{1}{2} \pi (4) \]
\[ \text{Area of Semicircle} = 2 \pi \, \text{cm}^2 \approx 6.28 \, \text{cm}^2 \]
3. **Total Area of the Shape:**
\[ \text{Total Area} = \text{Area of Rectangle} + \text{
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