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Find the area of a regular hexagon with side length $18$ inches.

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Solve proportions: word problems

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Q. Find the area of a regular hexagon with side length

18

inches.

Understand the formula: Understand the formula for the area of a regular hexagon. $\newline$ The area $A$ of a regular hexagon can be calculated using the formula: $\newline$ $A = \frac{3\sqrt{3}}{2} \cdot s^2$ $\newline$ where $s$ is the length of a side of the hexagon.
Plug side length: Plug the given side length into the formula. $\newline$ Given that the side length $s$ is $18$ inches, we can substitute this value into the formula: $\newline$ $A = \left(\frac{3\sqrt{3}}{2}\right) \times 18^2$
Calculate the area: Calculate the area. $\newline$ First, square the side length: $\newline$ $18^2 = 324$ $\newline$ Then, multiply by the constant $(3\sqrt{3}/2)$ : $\newline$ $A = (3\sqrt{3}/2) \times 324$
Simplify the calculation: Simplify the calculation. $\newline$ To simplify the calculation, we can first multiply $324$ by $3$ : $\newline$ $324 \times 3 = 972$ $\newline$ Now, divide by $2$ : $\newline$ $972 / 2 = 486$ $\newline$ Finally, multiply by $\sqrt{3}$ : $\newline$ $A = 486 \times \sqrt{3}$
Calculate final value: Calculate the final value. $\newline$ To get the exact area, we can leave the answer in terms of $\sqrt{3}$ : $\newline$ $A = 486\sqrt{3}$ square inches $\newline$ If a decimal approximation is needed, we can use the approximate value of $\sqrt{3}$ , which is about $1$ . $732$ : $\newline$ $A \approx 486 \times 1.732$ $\newline$ $A \approx 842.352$

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