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7. Euness wants to order new carpet for her living room. The living room is rectangular, with a triangle and rectangle missing, as shown. The dimensions are in feet. 16 ft 4 ft 3 ft 12 ft LIVING ROOM 4 ft 3 ft What is the area of the living room? A. 174 square feet B. 192 square feet C. 282 square feet D. 300 square feet

7. Euness wants to order new carpet for her living room. The living room is rectangular, with a triangle and rectangle missing, as shown. The dimensions are in feet. 16 ft 4 ft 3 ft 12 ft LIVING ROOM 4 ft 3 ft What is the area of the living room? A. 174 square feet B. 192 square feet C. 282 square feet D. 300 square feet

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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### Problem Description **Question 7:** Euness wants to order new carpet for her living room. The living room is rectangular, with a triangle and rectangle missing, as shown in the diagram. The dimensions are in feet. Diagram description: - The living room is a rectangular shape with dimensions 16 feet by 12 feet. - Two areas are subtracted from the rectangular shape: a smaller rectangle of 4 feet by 3 feet, and a right triangle with legs measuring 4 feet and 3 feet. - The missing triangle and rectangle are situated at the top and right-hand side of the diagram. **Question:** What is the area of the living room? **Answer Choices:** A. 174 square feet B. 192 square feet C. 282 square feet D. 300 square feet ### Detailed Graph/Diagram Explanation 1. **Original Rectangle:** - Length: 16 feet - Width: 12 feet - Area: \( 16 \times 12 = 192 \) square feet 2. **Subtracted Rectangle:** - Length: 4 feet - Width: 3 feet - Area: \( 4 \times 3 = 12 \) square feet 3. **Subtracted Triangle:** - Base: 4 feet - Height: 3 feet - Area: \( \frac{1}{2} \times 4 \times 3 = 6 \) square feet 4. **Net Area of Living Room:** - Area of original rectangle minus the areas of the subtracted rectangle and triangle: \( 192 - 12 - 6 = 174 \) square feet Thus, the correct answer is: **A. 174 square feet**
Transcribed Image Text:### Problem Description **Question 7:** Euness wants to order new carpet for her living room. The living room is rectangular, with a triangle and rectangle missing, as shown in the diagram. The dimensions are in feet. Diagram description: - The living room is a rectangular shape with dimensions 16 feet by 12 feet. - Two areas are subtracted from the rectangular shape: a smaller rectangle of 4 feet by 3 feet, and a right triangle with legs measuring 4 feet and 3 feet. - The missing triangle and rectangle are situated at the top and right-hand side of the diagram. **Question:** What is the area of the living room? **Answer Choices:** A. 174 square feet B. 192 square feet C. 282 square feet D. 300 square feet ### Detailed Graph/Diagram Explanation 1. **Original Rectangle:** - Length: 16 feet - Width: 12 feet - Area: \( 16 \times 12 = 192 \) square feet 2. **Subtracted Rectangle:** - Length: 4 feet - Width: 3 feet - Area: \( 4 \times 3 = 12 \) square feet 3. **Subtracted Triangle:** - Base: 4 feet - Height: 3 feet - Area: \( \frac{1}{2} \times 4 \times 3 = 6 \) square feet 4. **Net Area of Living Room:** - Area of original rectangle minus the areas of the subtracted rectangle and triangle: \( 192 - 12 - 6 = 174 \) square feet Thus, the correct answer is: **A. 174 square feet**
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