the area of the regular hexagon is 169.74 ft². what is the perimeter, rounded to the nearest tenth? 24.2 ft…

Explanation:

Step1: Recall area formula for regular hexagon

The area formula for a regular hexagon is $A = \frac{3\sqrt{3}}{2}s^{2}$, where $s$ is the side - length of the hexagon. Given $A = 169.74\ ft^{2}$. We set up the equation $\frac{3\sqrt{3}}{2}s^{2}=169.74$.

Step2: Solve for side - length $s$

First, we can rewrite the equation as $s^{2}=\frac{169.74\times2}{3\sqrt{3}}$. Calculate $\frac{169.74\times2}{3\sqrt{3}}=\frac{339.48}{3\sqrt{3}}\approx\frac{339.48}{3\times1.732}=\frac{339.48}{5.196} = 65.33487$. Then $s=\sqrt{65.33487}\approx 8.08\ ft$.

Step3: Calculate the perimeter $P$ of the hexagon

The perimeter of a hexagon is $P = 6s$. Substitute $s\approx8.08\ ft$ into the formula, we get $P = 6\times8.08 = 48.48\ ft\approx48.5\ ft$.

Answer:

48.5 ft