Question

Given a regular polygon with 9 sides, each side length is 25 cm what is the area? (the apothem is about 11.75cm)

Answer 1

To find the area of a regular polygon, you can use the formula:

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

1. **Calculate the Perimeter**:
The perimeter \( P \) of a regular polygon can be found by multiplying the number of sides \( n \) by the length of each side \( s \):

\[
P = n \times s
\]

For a polygon with 9 sides (n = 9) and each side measuring 25 cm:

\[
P = 9 \times 25 = 225 \text{ cm}
\]

2. **Use the Apothem**:
You mentioned that the apothem \( a \) is about 11.75 cm.

3. **Calculate the Area**:
Now plug these values into the area formula:

\[
\text{Area} = \frac{1}{2} \times P \times a
\]

\[
\text{Area} = \frac{1}{2} \times 225 \times 11.75
\]

\[
\text{Area} = \frac{1}{2} \times 2637.5 = 1318.75 \text{ cm}^2
\]

So, the area of the regular polygon with 9 sides and each side length of 25 cm is approximately \( 1318.75 \text{ cm}^2 \).