Question

how to solve this
fing the radius, the apothem, and the area of a decagon whose side is 10 inches???

Answer 1

http://en.wikipedia.org/wiki/Apothem That appears to have all the info you need to derive apothem, radius, and area.

Answer 2

decagon has 10 sides,if a= apothem,p=perimeter,s=side length,n=10,p=ns=10s=10(10)=100,
Area A=ap/2=asn/2,
but apothem a=s/2tan(pi/n)=10/2tan(pi/10)=15.39
Area A=asn/2=15.39(10)(10)/2=769.5
we can get tge radius from perimeter P=2(pi)r sin(180/n)
radius r=P/2pi sin(180/n)
=100/2pi sin(180/10)
=50/pi sin18
=51.5