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An architect creates the following blueprint for a deck being added to a house. Size Undo Clear All 17 ft 37⁰ 10 ft 12 ft 18 ft L Note: Figure not drawn to scale. 9 ft What is the approximate area of the deck? O266.3 ft² O 218.3 ft² O 207.3 ft² O 194.3 ft²

An architect creates the following blueprint for a deck being added to a house. Size Undo Clear All 17 ft 37⁰ 10 ft 12 ft 18 ft L Note: Figure not drawn to scale. 9 ft What is the approximate area of the deck? O266.3 ft² O 218.3 ft² O 207.3 ft² O 194.3 ft²

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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**Blueprint Analysis for Deck Addition** **Problem Statement:** An architect has created a blueprint for a deck that will be added to a house. The blueprint is provided below, along with a series of measurements. **Blueprint Diagram:** The diagram shows a two-dimensional layout of the proposed deck. Several measurements are provided, along with an angle measurement and a reminder that the figure is not drawn to scale. **Measurements Provided:** - The deck has a length of 18 feet on one side. - Another side of the deck measures 9 feet. - A section of the deck extends 12 feet with an adjacent 10-foot side. - The external extension measures 17 feet from top to bottom of this section. - It includes an angle of 37° along a curved section. **Notation:** There is a note indicating: "Figure not drawn to scale." **Question:** What is the approximate area of the deck? A. 266.3 ft² B. 218.3 ft² C. 207.3 ft² D. 194.3 ft² **Study Guide Explanation:** To determine the approximate area of this deck, recognize that the shape of the deck can be broken down into simpler geometric shapes, such as rectangles and a smaller triangular section. 1. **Identify Rectangles:** - The main rectangular section of the deck connects the 18 ft and 9 ft sides. - The extension that measures 12 ft by 17 ft. 2. **Identify Triangle and Other Sections:** - Consider the smaller triangular area defined by the 37° angle. 3. **Calculate Area:** - Use the formula for the area of rectangular sections: \( \text{Area} = \text{length} \times \text{width} \) - Calculate triangular area: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \) 4. **Sum the Areas:** - Combine areas of individual sections to get the total deck area. 5. **Approximation:** - Choose the answer closest to this calculation from the multiple-choice options provided. This strategy will help in understanding how to break complex figures into simpler components for area calculation.
Transcribed Image Text:**Blueprint Analysis for Deck Addition** **Problem Statement:** An architect has created a blueprint for a deck that will be added to a house. The blueprint is provided below, along with a series of measurements. **Blueprint Diagram:** The diagram shows a two-dimensional layout of the proposed deck. Several measurements are provided, along with an angle measurement and a reminder that the figure is not drawn to scale. **Measurements Provided:** - The deck has a length of 18 feet on one side. - Another side of the deck measures 9 feet. - A section of the deck extends 12 feet with an adjacent 10-foot side. - The external extension measures 17 feet from top to bottom of this section. - It includes an angle of 37° along a curved section. **Notation:** There is a note indicating: "Figure not drawn to scale." **Question:** What is the approximate area of the deck? A. 266.3 ft² B. 218.3 ft² C. 207.3 ft² D. 194.3 ft² **Study Guide Explanation:** To determine the approximate area of this deck, recognize that the shape of the deck can be broken down into simpler geometric shapes, such as rectangles and a smaller triangular section. 1. **Identify Rectangles:** - The main rectangular section of the deck connects the 18 ft and 9 ft sides. - The extension that measures 12 ft by 17 ft. 2. **Identify Triangle and Other Sections:** - Consider the smaller triangular area defined by the 37° angle. 3. **Calculate Area:** - Use the formula for the area of rectangular sections: \( \text{Area} = \text{length} \times \text{width} \) - Calculate triangular area: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \) 4. **Sum the Areas:** - Combine areas of individual sections to get the total deck area. 5. **Approximation:** - Choose the answer closest to this calculation from the multiple-choice options provided. This strategy will help in understanding how to break complex figures into simpler components for area calculation.
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