Question
What is the formula for the area of a regular hexagon?
Answers
GPT-4o mini
The formula for the area \( A \) of a regular hexagon (a hexagon with all sides and angles equal) can be calculated using the length of one side \( s \):
\[
A = \frac{3\sqrt{3}}{2} s^2
\]
Alternatively, if you know the apothem \( a \) (the distance from the center to the midpoint of a side) and the perimeter \( P \) of the hexagon, the area can also be calculated as:
\[
A = \frac{1}{2} \times P \times a
\]
For a regular hexagon, the perimeter \( P \) is given by \( P = 6s \). Thus, the area can also be expressed in terms of the apothem and side length as follows:
\[
A = \frac{3s \cdot a}{2}
\]
Using either formula, you can calculate the area of a regular hexagon based on the known measurements.
\[
A = \frac{3\sqrt{3}}{2} s^2
\]
Alternatively, if you know the apothem \( a \) (the distance from the center to the midpoint of a side) and the perimeter \( P \) of the hexagon, the area can also be calculated as:
\[
A = \frac{1}{2} \times P \times a
\]
For a regular hexagon, the perimeter \( P \) is given by \( P = 6s \). Thus, the area can also be expressed in terms of the apothem and side length as follows:
\[
A = \frac{3s \cdot a}{2}
\]
Using either formula, you can calculate the area of a regular hexagon based on the known measurements.