Posted by **Marjorie** on Tuesday, April 5, 2011 at 7:48pm.

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

- Geometry -
**bobpursley**, Tuesday, April 5, 2011 at 8:22pm
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

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