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To find the area of a regular octagon, we can use the formula:

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

### Step 1: Calculate the perimeter
The perimeter \( P \) of a regular octagon is given by the product of the number of sides (8) and the length of one side.

\[
P = 8 \times \text{side length} = 8 \times 8.3 \, \text{cm} = 66.4 \, \text{cm}
\]

### Step 2: Use the apothem and perimeter in the area formula
We are given that the apothem is 10 cm. Now we can substitute the values into the area formula:

\[
\text{Area} = \frac{1}{2} \times 66.4 \, \text{cm} \times 10 \, \text{cm} = \frac{1}{2} \times 664 \, \text{cm}^2 = 332 \, \text{cm}^2
\]

Thus, the area of the regular octagon is **332 cm²**.

Would you like further details, or do you have any questions?

Here are 5 related questions to explore:
1. How does the apothem relate to the side length of a regular polygon?
2. Can the formula for the area of a regular polygon be applied to other shapes like hexagons or pentagons?
3. How does changing the apothem affect the area of a regular polygon?
4. What is the geometric significance of the apothem in regular polygons?
5. How can the side length be calculated if only the apothem and area are known?

**Tip:** For regular polygons, the apothem is a helpful tool because it acts like the "height" when calculating the area.

Find the area of a regular octagon with an apothem of 10 cm and a side length of 8.3 cm.

Calculate the area of a regular octagon with an apothem of 10 cm and a side length of 8.3 cm using the formula: Area = 0.5 * Perimeter * Apothem. This problem helps understand polygon geometry and applies key concepts like apothem and perimeter in the area formula. Suitable for students in Grades 8-10.

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