SOLUTION: what is the area of a hexagon with an apothem of 4ft?

Question 324400: what is the area of a hexagon with an apothem of 4ft?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Using the properties of a 30-60-90 right triangle, you can readily determine that the measure of the apothem and the radius of the circumcircle (which is equal to the measure of a side of a regular hexagon) are in proportion:

Hence a regular hexagon with an apothem of 4 has a side that measures

.

The perimeter of such a hexagon is simply 6 times the measure of a side, and therefore half of the perimeter is 3 times the measure of a side.

The area of a hexagon with perimeter

and apothem

is given by:

John

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