#### Answer

13.1

#### Work Step by Step

When we break a regular decagon into 20 separate right triangles, each triangle has an angle of 18 degrees in it. Using this angle and the fact that the apothem is 12.5 inches, we find:
$cos18^{\circ}=\frac{12.5}{r} \\ r = \frac{12.5}{cos18^{\circ}} = 13.1$