Hesources Googie Docs oreat ooope dasoom Nearpod Welcome Meting is in progre O Reading lat Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place. 6. 4
Hesources Googie Docs oreat ooope dasoom Nearpod Welcome Meting is in progre O Reading lat Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place. 6. 4
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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![### Calculating the Area of Composite Shapes: Rectangle and Semicircle
**Objective:** To find the area of a composite figure consisting of a rectangle and a semicircle. Round to the nearest tenths place.
#### Step-by-Step Solution:
1. **Identifying the Components:**
The given figure consists of a rectangle with a semicircle attached to one of its sides.
2. **Dimensions Provided:**
- The length of the rectangle is 6 units.
- The height of the rectangle is 4 units.
#### Calculation of Areas:
1. **Area of the Rectangle:**
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 6 \, \text{units} \times 4 \, \text{units} = 24 \, \text{square units}
\]
2. **Area of the Semicircle:**
- The diameter of the semicircle is equal to the width of the rectangle, which is 4 units.
- Therefore, the radius \( r \) of the semicircle is:
\[
r = \frac{\text{diameter}}{2} = \frac{4 \, \text{units}}{2} = 2 \, \text{units}
\]
- The area of a full circle is given by \( \pi r^2 \).
- The area of the semicircle is half of the area of the full circle:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2 \, \text{units})^2 = \frac{1}{2} \pi \times 4 \, \text{square units} = 2 \pi \, \text{square units}
\]
- Approximating \(\pi \approx 3.14159\):
\[
\text{Area}_{\text{semicircle}} \approx 2 \times 3.14159 = 6.28318 \, \text{square units}
\]
3. **Total Area:**
- The total area of the composite figure is the sum of the area of the rectangle and the area of the semicircle:
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Transcribed Image Text:### Calculating the Area of Composite Shapes: Rectangle and Semicircle
**Objective:** To find the area of a composite figure consisting of a rectangle and a semicircle. Round to the nearest tenths place.
#### Step-by-Step Solution:
1. **Identifying the Components:**
The given figure consists of a rectangle with a semicircle attached to one of its sides.
2. **Dimensions Provided:**
- The length of the rectangle is 6 units.
- The height of the rectangle is 4 units.
#### Calculation of Areas:
1. **Area of the Rectangle:**
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 6 \, \text{units} \times 4 \, \text{units} = 24 \, \text{square units}
\]
2. **Area of the Semicircle:**
- The diameter of the semicircle is equal to the width of the rectangle, which is 4 units.
- Therefore, the radius \( r \) of the semicircle is:
\[
r = \frac{\text{diameter}}{2} = \frac{4 \, \text{units}}{2} = 2 \, \text{units}
\]
- The area of a full circle is given by \( \pi r^2 \).
- The area of the semicircle is half of the area of the full circle:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2 \, \text{units})^2 = \frac{1}{2} \pi \times 4 \, \text{square units} = 2 \pi \, \text{square units}
\]
- Approximating \(\pi \approx 3.14159\):
\[
\text{Area}_{\text{semicircle}} \approx 2 \times 3.14159 = 6.28318 \, \text{square units}
\]
3. **Total Area:**
- The total area of the composite figure is the sum of the area of the rectangle and the area of the semicircle:
\
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