Charles creates a rectangle with the dimensions 314 in by  123 in.  Calculate the area of the rectangle. Be sure to show all steps and follow the communication process demonstrated in class (vertical solutions, equal signs at the start of each line, answers in lowest terms). 



To find the area of a rectangle, we use the formula:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Given:
- Length = 314 inches
- Width = 123 inches

Now, let's calculate step by step.

\[
\text{Area} = 314 \times 123
\]

### Step-by-step multiplication:

\[
314 \times 123 = (314 \times 100) + (314 \times 20) + (314 \times 3)
\]

\[
314 \times 100 = 31400
\]
\[
314 \times 20 = 6280
\]
\[
314 \times 3 = 942
\]

Now, add them together:

\[
31400 + 6280 + 942 = 38622
\]

Thus, the area of the rectangle is:

\[
\boxed{38,622 \, \text{square inches}}
\]

Let me know if you'd like more details or have questions. Here are 5 related questions to expand this:

1. What would the perimeter of this rectangle be?
2. How would the area change if the width doubled?
3. Can you calculate the area of a square with the same perimeter as this rectangle?
4. What would be the area if the length and width were switched?
5. How does the area of this rectangle compare to one with dimensions 200 in by 200 in?

**Tip**: Always check for units in geometric problems to ensure consistency in your calculations.

Charles creates a rectangle with the dimensions 314 in by 123 in. Calculate the area of the rectangle. Be sure to show all steps and follow the communication process demonstrated in class (vertical solutions, equal signs at the start of each line, answers in lowest terms).

Learn how to calculate the area of a rectangle with dimensions 314 inches by 123 inches. This step-by-step solution covers essential geometry concepts and includes detailed multiplication breakdowns, making it suitable for students in Grades 5-7.

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