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The area of a regular hexagon is 60 in². Find the length of a side. Round your answer to the nearest tenth.
A. 23.1 in
B. 8.3 in
C. 6.3 in
D. 4.8 in

Respuesta :

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

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