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Terms Use Calculator The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? O 12+18.25 units² O 24+9.1257 units² O 24+18.257 units² O 12+9.125 units² 4-3-2-¹1. 4 2 1 1 -2+ -3+ -5+ 2 1 2 3 3 4 4 5 6 5 ➜X (O) 6 7

Terms Use Calculator The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? O 12+18.25 units² O 24+9.1257 units² O 24+18.257 units² O 12+9.125 units² 4-3-2-¹1. 4 2 1 1 -2+ -3+ -5+ 2 1 2 3 3 4 4 5 6 5 ➜X (O) 6 7

Elementary Geometry For College Students, 7e
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 a Combined Figure **Problem Statement:** The curved part of this figure is a semicircle. **Question:** What is the best approximation for the area of this figure? **Answer Choices:** - O 12 + 18.25π units² - O 24 + 9.125π units² - O 24 + 18.25π units² - O 12 + 9.125π units² **Diagram Explanation:** The accompanying diagram shows a coordinate plane with a combined shape consisting of a square and a semicircle. The square is positioned with its bottom-left corner at (-3, -3) and extends to (3, 3), making the side length of the square 6 units. The semicircle is placed on the top side of the square. **Steps to Approximate the Area:** 1. **Calculate the Area of the Square:** - Side length = 6 units - Area of the square = side length² = 6² = 36 units² 2. **Calculate the Area of the Semicircle:** - Diameter of the semicircle = side length of the square = 6 units - Radius of the semicircle = diameter / 2 = 6 / 2 = 3 units - Area of a full circle = π * radius² = π * (3)² = 9π units² - Area of the semicircle = (1/2) * Area of the full circle = (1/2) * 9π = 4.5π units² 3. **Combine the Areas:** - Total area = Area of the square + Area of the semicircle = 36 units² + 4.5π units² **Multiple Choice Concept:** When selecting the best approximation for the area, identify the correct combination of constants and π terms that closely match the calculation above. The correct answer should consider both the square's area (36 units²) and the semicircle's area (4.5π units²). **Answer:** Thus, the closest match for the area is: - **24 + 18.25π units²**
Transcribed Image Text:### Calculating the Area of a Combined Figure **Problem Statement:** The curved part of this figure is a semicircle. **Question:** What is the best approximation for the area of this figure? **Answer Choices:** - O 12 + 18.25π units² - O 24 + 9.125π units² - O 24 + 18.25π units² - O 12 + 9.125π units² **Diagram Explanation:** The accompanying diagram shows a coordinate plane with a combined shape consisting of a square and a semicircle. The square is positioned with its bottom-left corner at (-3, -3) and extends to (3, 3), making the side length of the square 6 units. The semicircle is placed on the top side of the square. **Steps to Approximate the Area:** 1. **Calculate the Area of the Square:** - Side length = 6 units - Area of the square = side length² = 6² = 36 units² 2. **Calculate the Area of the Semicircle:** - Diameter of the semicircle = side length of the square = 6 units - Radius of the semicircle = diameter / 2 = 6 / 2 = 3 units - Area of a full circle = π * radius² = π * (3)² = 9π units² - Area of the semicircle = (1/2) * Area of the full circle = (1/2) * 9π = 4.5π units² 3. **Combine the Areas:** - Total area = Area of the square + Area of the semicircle = 36 units² + 4.5π units² **Multiple Choice Concept:** When selecting the best approximation for the area, identify the correct combination of constants and π terms that closely match the calculation above. The correct answer should consider both the square's area (36 units²) and the semicircle's area (4.5π units²). **Answer:** Thus, the closest match for the area is: - **24 + 18.25π units²**
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