Find the area of a circle circumscribed about a regular hexagon with an apothem of 5 inches. Round to the nearest tenth

Answer 1

I am not certain of your comfort with this, however, knowing either the apotherm or the circumradius you can find the other.

circumradius * cos(180/n)=apotherm

so in this case, atotherm=5inches, n=6

so circumradius * cos(30)=5inches
radius= 5inches / .866

Now the area of the circumscribed circle is PI*radius^2

Neat stuff. Thank your teacher.
http://en.wikipedia.org/wiki/Apothem