A regular hexagon is composed of six congruent equilateral triangles. Divide this total area (60) over 6 to get the area of a single triangle
60/6 = 10
Each triangle has an area of 10 square inches. So A = 10. We'll use the formula for an area of an equilateral triangle to solve for 's' (the side length) to get the final answer.
\(A = \frac{\sqrt{3}}{4}*s^2\)
\(10 = \frac{\sqrt{3}}{4}*s^2\)
\(4*10 = 4*\frac{\sqrt{3}}{4}*s^2\)
\(40 = \sqrt{3}*s^2\)
\(\frac{40}{\sqrt{3}} = \frac{\sqrt{3}*s^2}{\sqrt{3}}\)
\(\frac{40}{\sqrt{3}} = s^2\)
\(s^2 = \frac{40}{\sqrt{3}}\)
\(s^2 \approx 23.094010767585\)
\(\sqrt{s^2} \approx \sqrt{23.094010767585}\)
\(s \approx 4.8056228282695\)
\(s \approx 4.8\)
Each triangle has a side length of approximately 4.8 inches. So the length of each side of the hexagon is also approximately 4.8 inches.
Final Answer: Choice D) 4.8 in
