To find the area of a regular decagon, we need to follow these steps:
1. Calculate the perimeter of the decagon:
The perimeter of a regular polygon can be found by multiplying the number of sides by the side length.
Given:
- The number of sides [tex]\( n = 10 \)[/tex] (since it's a decagon)
- The side length [tex]\( s = 3.25 \)[/tex] meters
Perimeter [tex]\( P \)[/tex] is calculated as follows:
[tex]\[
P = n \times s = 10 \times 3.25 = 32.5 \text{ meters}
\][/tex]
2. Calculate the area of the decagon:
The area [tex]\( A \)[/tex] of a regular polygon can be found using the formula:
[tex]\[
A = \frac{1}{2} \times \text{perimeter} \times \text{apothem}
\][/tex]
Given:
- Apothem [tex]\( a = 5 \)[/tex] meters
Plugging in the values we have:
[tex]\[
A = \frac{1}{2} \times 32.5 \times 5 = 81.25 \text{ square meters}
\][/tex]
3. Round the area to the nearest tenth:
The area calculated is 81.25 square meters. When rounding to the nearest tenth, we inspect the hundredths place, which is 5 in this case, prompting us to round up.
Therefore:
[tex]\[
A \approx 81.2 \text{ square meters}
\][/tex]
Final result:
So, the area of the regular decagon is [tex]\( 81.2 \)[/tex] square meters when rounded to the nearest tenth.
