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Answer:
A regular pentagon has five equal sides. To find the length of one side, we can use the formula:
Area = (1/2) * base * height
where "base" is the length of one side and "height" is the distance from the base to the opposite vertex.
Since a regular pentagon has five equal sides, the height is equal to the length of one side. So, we can set up the equation as follows:
Area = (1/2) * side * side
The area of a regular pentagon is 1/4 times the product of its apothem and its perimeter. The apothem is the distance from the center to any vertex, and the perimeter is the sum of the lengths of all five sides.
Area = (1/4)(apothem * perimeter)
We can use these two equations to solve for the length of one side:
(1/2)(side^2 = (1/4)(apothem * 5*side)
Now, we can solve for the side:
(1/2)(side^2 = (1/4)(apothem * 5*side)
side^2 = (1/8)(apothem * 5*side)
side^2 = (1/8)(5*side)
side^2 = (5/16)*side
side^2 = (5/8)*side
Taking the square root of both sides:
side = (5/8)^(1/2) * side
side = (5/8)^(1/2)
Finally, we can solve for the length of one side:
side = (5/8)^(1/2)