Question

find the area of a regular octagon with an apothem of 7 inches and a side length of 5.8 inches.

? \\(\text{in}^2\\)

Explanation:

Identify the given values

We are given a regular octagon with:

• Number of sides \(n = 8\)
• Side length \(s = 5.8\text{ inches}\)
• Apothem \(a = 7\text{ inches}\)

Calculate the perimeter

Using the Area of Regular Polygon concept, we first find the perimeter \(P\):

$$ P = n \cdot s = 8 \cdot 5.8 = 46.4\text{ inches} $$

Calculate the area

Using the Area of Regular Polygon formula with the Apothem \(a\):

$$ A = \frac{1}{2} \cdot P \cdot a $$

$$ A = \frac{1}{2} \cdot 46.4 \cdot 7 = 23.2 \cdot 7 = 162.4\text{ in}^2 $$

Answer:

Find the area of a regular octagon with an apothem of 7 inches and a side length of 5.8 inches.

<blank>162.4</blank> \(\text{in}^2\)