SOLUTION: The area of a particular regular hexagon is x^3 square units, where x is the measure of the distance from the center of the hexagon to the midpoint of a side. What is the side len

Algebra ->  Polygons -> SOLUTION: The area of a particular regular hexagon is x^3 square units, where x is the measure of the distance from the center of the hexagon to the midpoint of a side. What is the side len      Log On


   

Question 623197: The area of a particular regular hexagon is x^3 square units, where x is the measure of the distance from the center of the hexagon to the midpoint of a side. What is the side length of the hexagon?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a regular polygon is given by:
A+=+%281%2F2%29%2AP%2Aa where P = perimeter and a = the length of the apothem.
Note: The apothem is the distance from the center to the midpoint of a side.
In this problem, we'll find the perimeter then divide it by 6 (a regular hexagon has 6 equal sides.)
A+=+%281%2F2%29%2AP%2Aa Substitute A+=+x%5E3 and a+=+x
x%5E3+=+%281%2F2%29%2AP%2Ax Divide both sides by x.
x%5E2+=+%281%2F2%29%2AP Multiply both sides by 2.
2x%5E2+=+P
Now that we have the perimeter, P, we can divide by 6 to find the length of one side, S.
S+=+P%2F6
S+=+2x%5E2%2F6 Simplify.
S+=+x%5E2%2F3 or S+=+%281%2F3%29x%5E2