Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**What is the area of the shaded region? Use 3.14 for pi and round your answer to the tenths place.**
The image shows a diagram with a red shaded region. This region is a square with a quarter circle removed from the top left corner. The side lengths of the square are 12 cm each, and the quarter circle has a radius of 12 cm.
To find the area of the shaded region:
1. **Calculate the area of the square:**
\[
\text{Area of the square} = \text{side} \times \text{side} = 12 \, \text{cm} \times 12 \, \text{cm} = 144 \, \text{cm}^2
\]
2. **Calculate the area of the quarter circle:**
\[
\text{Area of the circle} = \pi \times \left(\text{radius}\right)^2 = 3.14 \times \left(12 \, \text{cm}\right)^2 = 3.14 \times 144 \, \text{cm}^2 = 452.16 \, \text{cm}^2
\]
\[
\text{Area of the quarter circle} = \frac{\text{Area of the circle}}{4} = \frac{452.16 \, \text{cm}^2}{4} = 113.04 \, \text{cm}^2
\]
3. **Subtract the area of the quarter circle from the area of the square to get the shaded region:**
\[
\text{Area of the shaded region} = \text{Area of the square} - \text{Area of the quarter circle} = 144 \, \text{cm}^2 - 113.04 \, \text{cm}^2 = 30.96 \, \text{cm}^2
\]
4. **Round the result to the tenths place:**
\[
31.0 \, \text{cm}^2
\]
Thus, the area of the shaded region is \( 31.0 \, \text{cm}^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9c7c84e-880a-4aeb-aa8e-f6bb771b9ae1%2F39b3bbc8-a047-4a54-81df-858bf770278f%2Fincznxg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**What is the area of the shaded region? Use 3.14 for pi and round your answer to the tenths place.**
The image shows a diagram with a red shaded region. This region is a square with a quarter circle removed from the top left corner. The side lengths of the square are 12 cm each, and the quarter circle has a radius of 12 cm.
To find the area of the shaded region:
1. **Calculate the area of the square:**
\[
\text{Area of the square} = \text{side} \times \text{side} = 12 \, \text{cm} \times 12 \, \text{cm} = 144 \, \text{cm}^2
\]
2. **Calculate the area of the quarter circle:**
\[
\text{Area of the circle} = \pi \times \left(\text{radius}\right)^2 = 3.14 \times \left(12 \, \text{cm}\right)^2 = 3.14 \times 144 \, \text{cm}^2 = 452.16 \, \text{cm}^2
\]
\[
\text{Area of the quarter circle} = \frac{\text{Area of the circle}}{4} = \frac{452.16 \, \text{cm}^2}{4} = 113.04 \, \text{cm}^2
\]
3. **Subtract the area of the quarter circle from the area of the square to get the shaded region:**
\[
\text{Area of the shaded region} = \text{Area of the square} - \text{Area of the quarter circle} = 144 \, \text{cm}^2 - 113.04 \, \text{cm}^2 = 30.96 \, \text{cm}^2
\]
4. **Round the result to the tenths place:**
\[
31.0 \, \text{cm}^2
\]
Thus, the area of the shaded region is \( 31.0 \, \text{cm}^2 \).
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