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
![**Educational Content: Calculating the Shaded Area**
To find the area of the shaded region in the figure, follow these steps. The figure consists of a circle with a square inside it.
### Circle:
- **Diameter:** Given as 16 cm.
- **Radius:** Half of the diameter, so 8 cm.
- **Area of the Circle:** Use the formula \(A = \pi r^2\), where \(\pi = 3.14\).
\[
A = 3.14 \times (8)^2 = 3.14 \times 64 = 200.96 \, \text{cm}^2
\]
### Square:
- **Side Length:** Given as 10 cm.
- **Area of the Square:** Use the formula \(A = s^2\).
\[
A = (10)^2 = 100 \, \text{cm}^2
\]
### Shaded Area:
The shaded area is the part of the circle that is not covered by the square.
- **Shaded Area Calculation:**
\[
\text{Shaded Area} = \text{Area of Circle} - \text{Area of Square}
\]
\[
\text{Shaded Area} = 200.96 - 100 = 100.96 \, \text{cm}^2
\]
Therefore, the area of the shaded region is **100.96 cm\(^2\)**, rounded to two decimal places. This calculation demonstrates how to find the difference between the area of a circle and an inscribed square.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F623b396d-263f-4ca9-bfd7-445804398e90%2F73cc4ac5-c607-4774-a5f4-4b27b6fd3180%2F0yhnsod_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Calculating the Shaded Area**
To find the area of the shaded region in the figure, follow these steps. The figure consists of a circle with a square inside it.
### Circle:
- **Diameter:** Given as 16 cm.
- **Radius:** Half of the diameter, so 8 cm.
- **Area of the Circle:** Use the formula \(A = \pi r^2\), where \(\pi = 3.14\).
\[
A = 3.14 \times (8)^2 = 3.14 \times 64 = 200.96 \, \text{cm}^2
\]
### Square:
- **Side Length:** Given as 10 cm.
- **Area of the Square:** Use the formula \(A = s^2\).
\[
A = (10)^2 = 100 \, \text{cm}^2
\]
### Shaded Area:
The shaded area is the part of the circle that is not covered by the square.
- **Shaded Area Calculation:**
\[
\text{Shaded Area} = \text{Area of Circle} - \text{Area of Square}
\]
\[
\text{Shaded Area} = 200.96 - 100 = 100.96 \, \text{cm}^2
\]
Therefore, the area of the shaded region is **100.96 cm\(^2\)**, rounded to two decimal places. This calculation demonstrates how to find the difference between the area of a circle and an inscribed square.
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