Find the radius of a circle circumscribed in a regular pentagon whose perimeter is 28 inches.
+128474
I think you must mean "inscribed" if the circle is inside the regular pentagon...
Look at this picture to get a good idea of the situation :
AE = 28/5 inches = 5.6 inches....so AM is 1/2 of this = 2.8 inches
Angle AFE = 360/5 = 72°.....so.....angle AFM is 1/2 of this = 36°
And angle BAE = 108°.....so......angle FAM is 1/2 of this = 54°
And FM is the radius of the circle which can be found using The Law of Sines
AM / sin AFM = FM / sin FAM
2.8 / sin 36° = FM / sin 54°
Rearrange as
FM = sin 54° * 2.8 / sin 36° ≈ 3.854 inches
