The central angle subtended by each side of the pentagon is 72°. The radii dissect the pentagon into five isosceles triangles, each having odd angle 72° and equal sides 10 inches.
area of each triangle = 10²sin(72°)/2 = 50sin(72°)
pentagon area = 5[50sin(72°)] = 250sin(72°)
sin(72°) = √[10 - 2√(5)]/4
pentagon area = 250√[10 + 2√(5)]/4 = (125/2)√[10 + 2√(5)] in²
That is approximately 238 in².
This link can help explain sin(72°):
http://whistleralley.com/polyhedra/pentagon.htm