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The figure below is a net for a right rectangular prism. Its surface area is 72 cm2 and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.

The figure below is a net for a right rectangular prism. Its surface area is 72 cm2 and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.

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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### Understanding the Net of a Rectangular Prism #### Problem Statement The figure below is a net for a right rectangular prism. Its surface area is 72 cm² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension. #### Net Diagram Explanation The net consists of 6 rectangles arranged in the following manner: - **Top side (labeled as 'A')**: Area = ? - **Two vertical sides**: - Left: 6 cm² - Right: 6 cm² - **Horizontal side below the top side**: Area = 12 cm² - **Bottom side (labeled as 'A')**: Area = ? - **Two vertical sides**: - Left: 12 cm² - Right: 12 cm² Additionally, some dimensions are given: - Width of the top rectangular face: 3 cm - Length of the vertical rectangular face on the side: 3 cm - Height of the vertical rectangular face on the side: 2 cm (on both sides) Given information includes: - Surface area of the prism: 72 cm² #### Questions 1. The area of each missing face is: - Area = __________ cm² 2. The length of each missing edge is: - Length = __________ cm ### Working Through the Solution 1. **Finding the Area of the Missing Faces**: - Start by calculating the area of each given face: - Two faces of 6 cm² each. - Two faces of 12 cm² each. - One face of 12 cm² (bottom). - Sum of the areas of the given faces: - \( 2 \times 6 \, \text{cm}^2 + 3 \times 12 \, \text{cm}^2 = 12 \, \text{cm}^2 + 36 \, \text{cm}^2 = 48 \, \text{cm}^2 \) - Since the total surface area is 72 cm², the area of the missing two faces is: \( 72 \, \text{cm}^2 - 48 \, \text{cm}^2 = 24 \, \text{cm}^2 \) - Each missing face has equal
Transcribed Image Text:### Understanding the Net of a Rectangular Prism #### Problem Statement The figure below is a net for a right rectangular prism. Its surface area is 72 cm² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension. #### Net Diagram Explanation The net consists of 6 rectangles arranged in the following manner: - **Top side (labeled as 'A')**: Area = ? - **Two vertical sides**: - Left: 6 cm² - Right: 6 cm² - **Horizontal side below the top side**: Area = 12 cm² - **Bottom side (labeled as 'A')**: Area = ? - **Two vertical sides**: - Left: 12 cm² - Right: 12 cm² Additionally, some dimensions are given: - Width of the top rectangular face: 3 cm - Length of the vertical rectangular face on the side: 3 cm - Height of the vertical rectangular face on the side: 2 cm (on both sides) Given information includes: - Surface area of the prism: 72 cm² #### Questions 1. The area of each missing face is: - Area = __________ cm² 2. The length of each missing edge is: - Length = __________ cm ### Working Through the Solution 1. **Finding the Area of the Missing Faces**: - Start by calculating the area of each given face: - Two faces of 6 cm² each. - Two faces of 12 cm² each. - One face of 12 cm² (bottom). - Sum of the areas of the given faces: - \( 2 \times 6 \, \text{cm}^2 + 3 \times 12 \, \text{cm}^2 = 12 \, \text{cm}^2 + 36 \, \text{cm}^2 = 48 \, \text{cm}^2 \) - Since the total surface area is 72 cm², the area of the missing two faces is: \( 72 \, \text{cm}^2 - 48 \, \text{cm}^2 = 24 \, \text{cm}^2 \) - Each missing face has equal
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