SOLUTION: How do you find the area of a hexagon with a side length of four inches?

Algebra ->  Surface-area -> SOLUTION: How do you find the area of a hexagon with a side length of four inches?       Log On


   

Question 723000: How do you find the area of a hexagon with a side length of four inches?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula A = 1/2 * a * P where P is the perimeter and a is the apothem.


That formula only works for a regular polygon - all sides equal.


The perimeter of the given hexagon is 24.


The apothem is a line segment drawn from the midpoint of a side to the middle of the hexagon. The apothem, 1/2 the base, and a line drawn from the middle of the hexagon to the vertex of the same side from which the apothem is drawn forms a 30 60 90 triangle. 1/2 the side length is the side opposite 30. And 1/2 the side length times square root of 3 is the the apothem (side opposite the 60 degree angle).


For this hexagon the apothem is 2%2Asqrt%283%29 so the area is 1%2F2+%2A+2%2Asqrt%283%29+%2A+24+=+24%2Asqrt%283%29+=+approximately+38.1+square+inches.