Use the rectangular prism to complete the table . Only 4-8 on the table is what I need assistance with please. **Understanding Rectangular Prisms: Completing Tables and Calculations**Rectangular prisms are three-dimensional figures with six faces, all of which are rectangles. The characteristics of a rectangular prism can be described using three dimensions: length (l), width (w), and height (h). The image provides an illustration of a rectangular prism and a table with four columns for different sets of dimensions and corresponding measurements such as Lateral Area, Surface Area, and Volume. ### Example Table of a Rectangular PrismColumn definitions:1. **Length (l)**: The measurement of the prism's longer side.2. **Width (w)**: The measurement of the prism's shorter side (base).3. **Height (h)**: The measurement from the base to the top of the prism.Note: Some values in the table are obscured.#### Table illustrating given and derived measurements:| | 1 | 2 | 3 | 4 ||----------------|----|----|----|----|| **Length** | 8 | 12 | 6 | 12 || **Width** | 3 | 5 | | 6 || **Height** | 4 | | 2 | 2 || **Lateral Area** | | | | || **Surface Area** | | | | || **Volume** | | | | 48 |#### Formulas Needed for Calculations:1. **Lateral Surface Area (LSA)**: \[ LSA = 2h(l + w) \] where $ l $, $ w $, and $ h $ are the length, width, and height of the rectangular prism, respectively.2. **Surface Area (SA)**: \[ SA = 2(lw + lh + wh) \] where $ l $, $ w $, and $ h $ are the length, width, and height of the rectangular prism, respectively.3. **Volume (V)**: \[ V = l \times w \times h \] where $ l $, $ w $, and $ h $ are the length, width, and height of the rectangular prism, respectively.### Applying Form **Multiplication Table with Missing Values**This image presents a partially filled multiplication table. Each cell displays the product of the values at the corresponding row and column.### Table Structure and Contents:| | | | | | ||---|---|---|---|---|---|| | **4** | **5** | **6** | **7** | **8** || **3** | 12 | | 18 | | 3 || **2** | 6 | 9 | | | 2 || **1** | | 5 | 4 | 4 | || **9** | 72 | | | 208 | || **10** | | 528 | | | 22 || **50** | | | 450 | | |### Explanation:- **Row Headers and Column Headers:** - The row headers represent the multiplicands (3, 2, 1, 9, 10, 50). - The column headers represent the multipliers (4, 5, 6, 7, 8).- **Filled Values:** - The products of the row headers (multiplicands) and column headers (multipliers) are provided. - Some cells are filled based on the multiplication of corresponding headers.- **Missing Values:** - Blanks indicate where the products are missing. These can be computed based on the row and column headers.### Interpreting the Table:To find the missing values, multiply the row header by the column header. For example:- The cell in the second row and fourth column would be $3 \times 6 = 18$.- Similarly, for the cell in the fifth row and first column, the value is missing; hence it should be $9 \times 4 = 36$.This table helps students practice multiplication and understand the relationships between different numbers. Fill in the blanks to complete the table and verify your multiplications!

For a rectangular prism we have Surface area : 2(lw + lh + wh) Lateral surface area: 2(l+w) h Volume…

Answered: 4 6. 12 16 6. 4 72 528

Math

Geometry

4 6. 12 16 6. 4 72 528

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 4-8 on the table is what I need assistance with please.

**Understanding Rectangular Prisms: Completing Tables and Calculations**

Rectangular prisms are three-dimensional figures with six faces, all of which are rectangles. The characteristics of a rectangular prism can be described using three dimensions: length (l), width (w), and height (h).

The image provides an illustration of a rectangular prism and a table with four columns for different sets of dimensions and corresponding measurements such as Lateral Area, Surface Area, and Volume.

### Example Table of a Rectangular Prism

Column definitions:
1. **Length (l)**: The measurement of the prism's longer side.
2. **Width (w)**: The measurement of the prism's shorter side (base).
3. **Height (h)**: The measurement from the base to the top of the prism.

Note: Some values in the table are obscured.

#### Table illustrating given and derived measurements:

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

#### Formulas Needed for Calculations:

1. **Lateral Surface Area (LSA)**:
\[
LSA = 2h(l + w)
\]
where $ l $, $ w $, and $ h $ are the length, width, and height of the rectangular prism, respectively.

2. **Surface Area (SA)**:
\[
SA = 2(lw + lh + wh)
\]
where $ l $, $ w $, and $ h $ are the length, width, and height of the rectangular prism, respectively.

3. **Volume (V)**:
\[
V = l \times w \times h
\]
where $ l $, $ w $, and $ h $ are the length, width, and height of the rectangular prism, respectively.

### Applying Form

**Multiplication Table with Missing Values**

This image presents a partially filled multiplication table. Each cell displays the product of the values at the corresponding row and column.

### Table Structure and Contents:

| | | | | | |
|---|---|---|---|---|---|
| | **4** | **5** | **6** | **7** | **8** |
| **3** | 12 | | 18 | | 3 |
| **2** | 6 | 9 | | | 2 |
| **1** | | 5 | 4 | 4 | |
| **9** | 72 | | | 208 | |
| **10** | | 528 | | | 22 |
| **50** | | | 450 | | |

### Explanation:

- **Row Headers and Column Headers:**
- The row headers represent the multiplicands (3, 2, 1, 9, 10, 50).
- The column headers represent the multipliers (4, 5, 6, 7, 8).
- **Filled Values:**
- The products of the row headers (multiplicands) and column headers (multipliers) are provided.
- Some cells are filled based on the multiplication of corresponding headers.
- **Missing Values:**
- Blanks indicate where the products are missing. These can be computed based on the row and column headers.

### Interpreting the Table:

To find the missing values, multiply the row header by the column header. For example:
- The cell in the second row and fourth column would be $3 \times 6 = 18$.
- Similarly, for the cell in the fifth row and first column, the value is missing; hence it should be $9 \times 4 = 36$.

This table helps students practice multiplication and understand the relationships between different numbers. Fill in the blanks to complete the table and verify your multiplications!

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