### Educational Website Content---#### Understanding Rectangular Prisms through NetsThe figure below represents a net for a right rectangular prism. The total surface area of this prism is 222 cm². Given the areas of some of the faces, your task is to determine the area of the missing faces and the length of the missing dimension.![Net of a Rectangular Prism](image-link)##### Description:- This net consists of six faces that, when folded, form the rectangular prism.- The areas and some dimensions of the faces are given, with missing values denoted by '?'. ##### Given data:- Total surface area: 222 cm²- Known areas: - Two faces with an area of 63 cm² - Two faces with an area of 27 cm²- Dimensions: - Length of one edge: 7 cm - Length of other edges indicated: 9 cm##### Problem:- **Find the area of each missing face.**- **Determine the length of the missing edge.**###### Diagram Details:- The net is composed of three pairs of rectangular faces.- Dimensions of these rectangles and their corresponding areas are labelled, providing clues towards unknown values.---**Interactive Section:****Calculate the Missing Values:**1. **The area of each missing face is:** - Fill in the blank: `______ cm²` 2. **The length of each missing edge is:** - Fill in the blank: `______ cm`---In solving this problem, you will use your knowledge of surface area and rectangular prism properties to deduce the missing measurements and demonstrate an understanding of geometric relationships.---**End of Educational Content**

Answered: Image /qna-images/answer/7b8c7f4c-d31a-4759-914c-310e24192857.jpg

The figure below is a net for a right rectangular prism. Its surface area is 222 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 222 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

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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### Educational Website Content

---

#### Understanding Rectangular Prisms through Nets

The figure below represents a net for a right rectangular prism. The total surface area of this prism is 222 cm². Given the areas of some of the faces, your task is to determine the area of the missing faces and the length of the missing dimension.

![Net of a Rectangular Prism](image-link)

##### Description:
- This net consists of six faces that, when folded, form the rectangular prism.
- The areas and some dimensions of the faces are given, with missing values denoted by '?'.

##### Given data:
- Total surface area: 222 cm²
- Known areas:
- Two faces with an area of 63 cm²
- Two faces with an area of 27 cm²
- Dimensions:
- Length of one edge: 7 cm
- Length of other edges indicated: 9 cm

##### Problem:
- **Find the area of each missing face.**
- **Determine the length of the missing edge.**

###### Diagram Details:
- The net is composed of three pairs of rectangular faces.
- Dimensions of these rectangles and their corresponding areas are labelled, providing clues towards unknown values.

---

**Interactive Section:**

**Calculate the Missing Values:**

1. **The area of each missing face is:**
- Fill in the blank: `______ cm²`

2. **The length of each missing edge is:**
- Fill in the blank: `______ cm`

---

In solving this problem, you will use your knowledge of surface area and rectangular prism properties to deduce the missing measurements and demonstrate an understanding of geometric relationships.

---

**End of Educational Content**

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