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.
[tex]A = \frac{\sqrt{3}}{4}*s^2[/tex]
[tex]10 = \frac{\sqrt{3}}{4}*s^2[/tex]
[tex]4*10 = 4*\frac{\sqrt{3}}{4}*s^2[/tex]
[tex]40 = \sqrt{3}*s^2[/tex]
[tex]\frac{40}{\sqrt{3}} = \frac{\sqrt{3}*s^2}{\sqrt{3}}[/tex]
[tex]\frac{40}{\sqrt{3}} = s^2[/tex]
[tex]s^2 = \frac{40}{\sqrt{3}}[/tex]
[tex]s^2 \approx 23.094010767585[/tex]
[tex]\sqrt{s^2} \approx \sqrt{23.094010767585}[/tex]
[tex]s \approx 4.8056228282695[/tex]
[tex]s \approx 4.8[/tex]
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
