Question
How do I calculate the area of a regular hexagon with a side length of 6 cm?
Answers
GPT-4o mini
To calculate the area of a regular hexagon, you can use the formula:
\[
\text{Area} = \frac{3\sqrt{3}}{2} s^2
\]
where \( s \) is the length of a side of the hexagon.
For a regular hexagon with a side length of 6 cm:
1. Substitute \( s = 6 \) into the formula:
\[
\text{Area} = \frac{3\sqrt{3}}{2} (6)^2
\]
2. Calculate \( (6)^2 \):
\[
(6)^2 = 36
\]
3. Now, substitute that value back into the formula:
\[
\text{Area} = \frac{3\sqrt{3}}{2} \times 36
\]
4. Multiply:
\[
\text{Area} = 54\sqrt{3}
\]
5. If you want a numerical approximation, you can calculate \( \sqrt{3} \approx 1.732 \):
\[
\text{Area} \approx 54 \times 1.732 \approx 93.53 \text{ cm}^2
\]
Thus, the area of the regular hexagon with a side length of 6 cm is \( 54\sqrt{3} \) cm² or approximately \( 93.53 \) cm².
\[
\text{Area} = \frac{3\sqrt{3}}{2} s^2
\]
where \( s \) is the length of a side of the hexagon.
For a regular hexagon with a side length of 6 cm:
1. Substitute \( s = 6 \) into the formula:
\[
\text{Area} = \frac{3\sqrt{3}}{2} (6)^2
\]
2. Calculate \( (6)^2 \):
\[
(6)^2 = 36
\]
3. Now, substitute that value back into the formula:
\[
\text{Area} = \frac{3\sqrt{3}}{2} \times 36
\]
4. Multiply:
\[
\text{Area} = 54\sqrt{3}
\]
5. If you want a numerical approximation, you can calculate \( \sqrt{3} \approx 1.732 \):
\[
\text{Area} \approx 54 \times 1.732 \approx 93.53 \text{ cm}^2
\]
Thus, the area of the regular hexagon with a side length of 6 cm is \( 54\sqrt{3} \) cm² or approximately \( 93.53 \) cm².