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To solve the problem of finding the apothem of a regular polygon given the area and perimeter, we can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]

Given:
- Area \( A = 710.37 \) square units
- Perimeter \( P = 231.83 \) units

We can rearrange the formula to solve for the apothem \( a \):

\[
a = \frac{2 \times \text{Area}}{\text{Perimeter}}
\]

Substituting the given values:

\[
a = \frac{2 \times 710.37}{231.83}
\]

Now let's calculate the apothem.The apothem of the regular polygon is approximately **6.13 units**.

Would you like further details or have any additional questions?

Here are five related questions you might find interesting:
1. How does the number of sides of the polygon affect the length of the apothem?
2. What is the relationship between the apothem and the circumradius of a regular polygon?
3. How would the apothem change if the area was doubled while keeping the perimeter constant?
4. Can you derive the formula for the area of a regular polygon using the apothem?
5. How does the apothem help in finding the side length of a regular polygon?

**Tip:** The apothem is particularly useful in calculating the area of regular polygons because it relates directly to the radius of the inscribed circle.

What is the apothem of a regular polygon with an area of 710.37 sq. units and a perimeter of 231.83 units? Just type the numeric answer (Rounded to two decimal places).

Find out how to calculate the apothem of a regular polygon with a given area of 710.37 square units and a perimeter of 231.83 units. Understand the relationship between area, perimeter, and the apothem using key geometric formulas. Suitable for high school students in Grades 9-12.

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