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Answer :
To find the area of a regular pentagon with a given apothem and side length, you can follow these steps:
1. Understand the parameters of the problem:
- You have a regular pentagon, which means it has 5 equal sides.
- The apothem (the distance from the center to the middle of a side) is [tex]\( a = 24.7 \)[/tex] cm.
- The side length of the pentagon is [tex]\( s = 35.9 \)[/tex] cm.
2. Use the formula for the area of a regular polygon:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\][/tex]
3. Calculate the perimeter of the pentagon:
- Since the pentagon has 5 sides each of length [tex]\( s \)[/tex], the perimeter [tex]\( P \)[/tex] is:
[tex]\[
P = 5 \times s = 5 \times 35.9 \text{ cm} = 179.5 \text{ cm}
\][/tex]
4. Substitute the values into the area formula:
- Now you can find the area using the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times P \times a = \frac{1}{2} \times 179.5 \times 24.7
\][/tex]
5. Calculate the area:
- Carry out the multiplication:
[tex]\[
\text{Area} = \frac{1}{2} \times 179.5 \times 24.7 = 2216.825 \text{ cm}^2
\][/tex]
6. Round the result:
- Round this to three decimal places to get:
[tex]\[
\text{Area} = 2216.825 \text{ cm}^2
\][/tex]
So, the area of the regular pentagon is approximately [tex]\( 2216.825 \)[/tex] cm².
1. Understand the parameters of the problem:
- You have a regular pentagon, which means it has 5 equal sides.
- The apothem (the distance from the center to the middle of a side) is [tex]\( a = 24.7 \)[/tex] cm.
- The side length of the pentagon is [tex]\( s = 35.9 \)[/tex] cm.
2. Use the formula for the area of a regular polygon:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\][/tex]
3. Calculate the perimeter of the pentagon:
- Since the pentagon has 5 sides each of length [tex]\( s \)[/tex], the perimeter [tex]\( P \)[/tex] is:
[tex]\[
P = 5 \times s = 5 \times 35.9 \text{ cm} = 179.5 \text{ cm}
\][/tex]
4. Substitute the values into the area formula:
- Now you can find the area using the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times P \times a = \frac{1}{2} \times 179.5 \times 24.7
\][/tex]
5. Calculate the area:
- Carry out the multiplication:
[tex]\[
\text{Area} = \frac{1}{2} \times 179.5 \times 24.7 = 2216.825 \text{ cm}^2
\][/tex]
6. Round the result:
- Round this to three decimal places to get:
[tex]\[
\text{Area} = 2216.825 \text{ cm}^2
\][/tex]
So, the area of the regular pentagon is approximately [tex]\( 2216.825 \)[/tex] cm².
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