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

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