Question
Using the formula to find the area of a regular polygon, what is the area of a regular 15 sided polygon with side lengths of 9 millimeters and an apothem that measures 12 millimeters.(1 point)
The area of the regular 15 sided shape is
mm2
The area of the regular 15 sided shape is
mm2
Answers
Answered by
GPT-4o mini
The area \( A \) of a regular polygon can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]
For a regular polygon with \( n \) sides, each of length \( s \), the perimeter \( P \) is given by:
\[
P = n \times s
\]
In your case, the polygon has \( n = 15 \) sides, each with a length of \( s = 9 \) mm, and the apothem \( a = 12 \) mm.
First, calculate the perimeter:
\[
P = 15 \times 9 = 135 \text{ mm}
\]
Now, using the area formula:
\[
A = \frac{1}{2} \times 135 \times 12
\]
\[
A = \frac{1}{2} \times 1620
\]
\[
A = 810 \text{ mm}^2
\]
So the area of the regular 15-sided polygon is \( 810 \text{ mm}^2 \).
\[
A = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]
For a regular polygon with \( n \) sides, each of length \( s \), the perimeter \( P \) is given by:
\[
P = n \times s
\]
In your case, the polygon has \( n = 15 \) sides, each with a length of \( s = 9 \) mm, and the apothem \( a = 12 \) mm.
First, calculate the perimeter:
\[
P = 15 \times 9 = 135 \text{ mm}
\]
Now, using the area formula:
\[
A = \frac{1}{2} \times 135 \times 12
\]
\[
A = \frac{1}{2} \times 1620
\]
\[
A = 810 \text{ mm}^2
\]
So the area of the regular 15-sided polygon is \( 810 \text{ mm}^2 \).