Question
If you have a regular polygon with 11 sides and the sides are each 15cm what is the area of the polygon the Apothem is roughly 11.99 cm
Answers
GPT-4o mini
To find the area of a regular polygon, you can use the formula:
\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]
For an 11-sided polygon (a hendecagon) with each side measuring 15 cm, you can first calculate the perimeter:
\[
\text{Perimeter} = \text{number of sides} \times \text{length of each side} = 11 \times 15 \text{ cm} = 165 \text{ cm}
\]
Given the apothem is approximately 11.99 cm, you can now plug these values into the area formula:
\[
\text{Area} = \frac{1}{2} \times 165 \text{ cm} \times 11.99 \text{ cm}
\]
Calculating this step-by-step:
\[
\text{Area} = \frac{1}{2} \times 165 \times 11.99 \approx \frac{1}{2} \times 1978.35 \text{ cm}^2 \approx 989.175 \text{ cm}^2
\]
Therefore, the area of the regular polygon is approximately:
\[
\text{Area} \approx 989.18 \text{ cm}^2
\]
\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]
For an 11-sided polygon (a hendecagon) with each side measuring 15 cm, you can first calculate the perimeter:
\[
\text{Perimeter} = \text{number of sides} \times \text{length of each side} = 11 \times 15 \text{ cm} = 165 \text{ cm}
\]
Given the apothem is approximately 11.99 cm, you can now plug these values into the area formula:
\[
\text{Area} = \frac{1}{2} \times 165 \text{ cm} \times 11.99 \text{ cm}
\]
Calculating this step-by-step:
\[
\text{Area} = \frac{1}{2} \times 165 \times 11.99 \approx \frac{1}{2} \times 1978.35 \text{ cm}^2 \approx 989.175 \text{ cm}^2
\]
Therefore, the area of the regular polygon is approximately:
\[
\text{Area} \approx 989.18 \text{ cm}^2
\]