Geometry
posted by Marjorie .
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
Respond to this Question
Similar Questions

Math/Geometry
Can you help me with this? Find the area of each regular polygon. Round to the nearest tenth. 1. an equilateral triangle with an apothem 8.9 inches long 
geometry
a regular hexagon is inscribed in a circle. The radius of the circle is 18 units. What is the area of the region bounded by the inside of the circle and the outside of the hexagon. Round your answer to the nearest hundredth. 
geometry
find the area of a regular hexagon with the side length 4m. round to the nearest tenth 
Geometry
Find the area of a regular hexagon with side length of 10 centimeters. Round to the nearest tenth. 
Geometry
Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches. So far I each side of pentagon is 10. How do I find the radius of the circle? 
geometry
in order to find the area of a regular hexagon using the formula Area=1/2(nxs)(a)you must frist find the apothem whie vertical leg of a 306090 triangle with the base of 3. Find the length of the apothem in the 306090 triangle 
Geometry
Please Help Me! Find the area of this polygon rround to the nearest tenth. The polygon is a hexagon with six sides, and all they give is the apothem which is 6 inches long, what is the area? 
help hexagon geometry
A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon? 
Geometry  Area
Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your answer to the nearest tenth. 
GEOM B
Check over my answers? 28. A kite has diagonals 7.8 ft and 6 ft. What is the area of the kite?