Question

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

Answer 1

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 = (√(3))/(4)*s^2`


`10 = (√(3))/(4)*s^2`


`4*10 = 4*(√(3))/(4)*s^2`


`40 = √(3)*s^2`


`(40)/(√(3)) = (√(3)*s^2)/(√(3))`


`(40)/(√(3)) = s^2`


`s^2 = (40)/(√(3))`


`s^2 \approx 23.094010767585`


`√(s^2) \approx √(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