Use the rectangular prism to complete the table . Only 7& 8 on the table is what I need assistance with please. ### Using the Rectangular Prism to Complete the TableThis instructional guide will help you understand how to use the dimensions of a rectangular prism (a box-shaped geometric figure) to complete a table with various geometric properties. Let's first define the three dimensions of the prism:- **Length (l)**- **Width (w)**- **Height (h)**These dimensions are essential for computing surface area, lateral area, and volume. Here’s a diagram illustrating these dimensions:![Rectangular Prism](rectangular_prism_diagram.jpg)*(Diagram showing length (l), width (w), and height (h) of a rectangular prism)*Below is the partially completed table for different rectangular prisms. The first row lists the properties, and subsequent columns represent different instances of rectangular prisms with varying dimensions:| | 1 | 2 | 3 | 4 ||:-:|:-:|:-:|:-:|:-:||**Length**| 8 | 12 | 6 | 12 ||**Width**| 3 | 5 | 6 | 6 ||**Height**| 4 | 3 | 2 | 2 ||**Lateral Area**| ~ | ~ | ~ | ~ ||**Surface Area**| ~ | ~ | ~ | ~ ||**Volume**| ~ | ~ | ~ | 48 |### Descriptions of Properties (to be calculated):1. **Lateral Area**: This is the sum of the areas of the vertical sides (excluding the top and bottom faces) of the rectangular prism. - Formula: $ Lateral Area = 2h(l + w) $2. **Surface Area**: This is the sum of the areas of all six faces of the rectangular prism. - Formula: $ Surface Area = 2(lw + lh + wh) $3. **Volume**: This measures the capacity of the rectangular prism. - Formula: $ Volume = l \times w \times h $### Example Calculations:For the given dimensions, we can compute the various properties accordingly. Here, provided values are assumed known, whereas some values have been intentionally scribbled to indicate placeholders for further calculations.#### Calculation for Column 1- Length (l) = 8- Width (w) = 3- Height (h) = 4 The image shows a partial table structure with various numerical entries. Below is the transcription for educational purposes:| | ||---|---|| 7 | 8 || 18 | 3 || | 2 || 4 | || 208 | || | 22 |**Description of the table:**- The table displays two columns and a series of rows, some with numeric values and some left blank.- The first column includes the numbers: 7, 18, blank, 4, 208, and blank.- The second column includes the numbers: 8, 3, 2, blank, blank, and 22.This table might be used for a variety of educational purposes, such as illustrating mathematical operations, data organization, or even logic exercises where students need to deduce or fill in missing values.

Answered: Image /qna-images/answer/c79d8ed9-64b1-40fd-8284-8bee1a671e53.jpg

Answered: 8. 18 4 208 22 3.

Math

Geometry

8. 18 4 208 22 3.

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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Question

Use the rectangular prism to complete the table . Only 7& 8 on the table is what I need assistance with please.

### Using the Rectangular Prism to Complete the Table

This instructional guide will help you understand how to use the dimensions of a rectangular prism (a box-shaped geometric figure) to complete a table with various geometric properties. Let's first define the three dimensions of the prism:

- **Length (l)**
- **Width (w)**
- **Height (h)**

These dimensions are essential for computing surface area, lateral area, and volume. Here’s a diagram illustrating these dimensions:

![Rectangular Prism](rectangular_prism_diagram.jpg)
*(Diagram showing length (l), width (w), and height (h) of a rectangular prism)*

Below is the partially completed table for different rectangular prisms. The first row lists the properties, and subsequent columns represent different instances of rectangular prisms with varying dimensions:

| | 1 | 2 | 3 | 4 |
|:-:|:-:|:-:|:-:|:-:|
|**Length**| 8 | 12 | 6 | 12 |
|**Width**| 3 | 5 | 6 | 6 |
|**Height**| 4 | 3 | 2 | 2 |
|**Lateral Area**| ~ | ~ | ~ | ~ |
|**Surface Area**| ~ | ~ | ~ | ~ |
|**Volume**| ~ | ~ | ~ | 48 |

### Descriptions of Properties (to be calculated):

1. **Lateral Area**: This is the sum of the areas of the vertical sides (excluding the top and bottom faces) of the rectangular prism.
- Formula: $ Lateral Area = 2h(l + w) $

2. **Surface Area**: This is the sum of the areas of all six faces of the rectangular prism.
- Formula: $ Surface Area = 2(lw + lh + wh) $

3. **Volume**: This measures the capacity of the rectangular prism.
- Formula: $ Volume = l \times w \times h $

### Example Calculations:

For the given dimensions, we can compute the various properties accordingly. Here, provided values are assumed known, whereas some values have been intentionally scribbled to indicate placeholders for further calculations.

#### Calculation for Column 1
- Length (l) = 8
- Width (w) = 3
- Height (h) = 4

The image shows a partial table structure with various numerical entries. Below is the transcription for educational purposes:

| | |
|---|---|
| 7 | 8 |
| 18 | 3 |
| | 2 |
| 4 | |
| 208 | |
| | 22 |

**Description of the table:**

- The table displays two columns and a series of rows, some with numeric values and some left blank.
- The first column includes the numbers: 7, 18, blank, 4, 208, and blank.
- The second column includes the numbers: 8, 3, 2, blank, blank, and 22.

This table might be used for a variety of educational purposes, such as illustrating mathematical operations, data organization, or even logic exercises where students need to deduce or fill in missing values.

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