Question: A regular hexagon has one side that measures $6$ inches. What is the area of the hexagon?
A)
$3\sqrt{27}$ inches$^2$
B)
$54$ inches$^2$
C)
$54\sqrt{3}$ inches$^2$
D)
It cannot be determined from the given information. can you give me a similar problem
1. **State the problem:** We need to find the area of a regular hexagon with side length $6$ inches.
2. **Formula for the area of a regular hexagon:** The area $A$ of a regular hexagon with side length $s$ is given by:
$$A = \frac{3\sqrt{3}}{2} s^2$$
3. **Apply the formula:** Substitute $s = 6$ into the formula:
$$A = \frac{3\sqrt{3}}{2} \times 6^2$$
4. **Calculate the square of the side:**
$$6^2 = 36$$
5. **Substitute and simplify:**
$$A = \frac{3\sqrt{3}}{2} \times 36$$
6. **Multiply numerator and denominator:**
$$A = 3\sqrt{3} \times \cancel{\frac{36}{2}}^{18}$$
7. **Final multiplication:**
$$A = 54\sqrt{3}$$
8. **Interpretation:** The area of the regular hexagon is $54\sqrt{3}$ square inches.
**Answer:** Option C) $54\sqrt{3}$ inches$^2$.
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**Similar problem:**
Find the area of a regular hexagon with side length $8$ inches.