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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Help with this plz
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### Area of Segment
**Date and Time:**
Jun 18, 6:55:29 PM
---
**Problem Statement:**
Find the area of the shaded circle segment to the nearest tenth.
---
**Diagram Explanation:**
The diagram shows a circle with a sector labeled SRT included within it. The central angle \( \angle SRT = 90^\circ \). The radius of the circle is given as 1 cm. The shaded area is the minor segment formed by the chord ST and arc ST.
---
**Submission Field:**
```
Answer: [_________] cm² [Submit Answer]
```
---
- Attempts: 3 out of 4
- Problem: 1 out of many
---
**Explanation:**
To find the area of the shaded segment:
1. **Area of the sector SRT**:
\[
A_{\text{sector}} = \left( \frac{\theta}{360^\circ} \right) \pi r^2
\]
where \( \theta = 90^\circ \) and \( r = 1 \) cm.
\[
A_{\text{sector}} = \left( \frac{90^\circ}{360^\circ} \right) \pi (1)^2 = \frac{1}{4} \pi \approx 0.7854 \text{ cm}^2
\]
2. **Area of triangle SRT**:
Since \( \angle SRT \) is a right angle, the area of the triangle is given by:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 1 = 0.5 \text{ cm}^2
\]
3. **Area of the shaded segment**:
\[
A_{\text{segment}} = A_{\text{sector}} - A_{\text{triangle}} = \frac{1}{4} \pi - 0.5 \approx 0.7854 - 0.5 = 0.2854 \text{ cm}^2
\]
To the nearest tenth, \( A_{\text{segment}} \approx 0.3 \text{ cm}^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fb42b59-2abc-4047-983a-bfb263ef58de%2F611d6d86-6de0-43c8-9b0d-a86a025333de%2Fdv1l4ca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Area of Segment
**Date and Time:**
Jun 18, 6:55:29 PM
---
**Problem Statement:**
Find the area of the shaded circle segment to the nearest tenth.
---
**Diagram Explanation:**
The diagram shows a circle with a sector labeled SRT included within it. The central angle \( \angle SRT = 90^\circ \). The radius of the circle is given as 1 cm. The shaded area is the minor segment formed by the chord ST and arc ST.
---
**Submission Field:**
```
Answer: [_________] cm² [Submit Answer]
```
---
- Attempts: 3 out of 4
- Problem: 1 out of many
---
**Explanation:**
To find the area of the shaded segment:
1. **Area of the sector SRT**:
\[
A_{\text{sector}} = \left( \frac{\theta}{360^\circ} \right) \pi r^2
\]
where \( \theta = 90^\circ \) and \( r = 1 \) cm.
\[
A_{\text{sector}} = \left( \frac{90^\circ}{360^\circ} \right) \pi (1)^2 = \frac{1}{4} \pi \approx 0.7854 \text{ cm}^2
\]
2. **Area of triangle SRT**:
Since \( \angle SRT \) is a right angle, the area of the triangle is given by:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 1 = 0.5 \text{ cm}^2
\]
3. **Area of the shaded segment**:
\[
A_{\text{segment}} = A_{\text{sector}} - A_{\text{triangle}} = \frac{1}{4} \pi - 0.5 \approx 0.7854 - 0.5 = 0.2854 \text{ cm}^2
\]
To the nearest tenth, \( A_{\text{segment}} \approx 0.3 \text{ cm}^2 \).
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