Based on the "information" given, one might expect the area to be

5*(1/2)*(6 in)*(5 in)*because[36°] ≈ 60.68 in^2 (The area of each of 5 triangles is 1/2*base*height.)

However, the formula for the area based on side length gives

A = (5/4)*(6 in)^2*Tan[54°] ≈ 61.94 in^2

The area based on the radius of the circumscribing circle is

A = (5/2)*(5 in)^2*Sin[72°] ≈ 59.44 in^2

In short, the given "information" is inconsistent.

If the side length of a regular pentagon is 6 inches, the distance from a vertex to the center is about 5.1039 inches (not 5 inches). If the distance from the center to a vertex is 5 inches, the length of a side will be about 5.8779 inches (not 6 inches).

5*(1/2)*(6 in)*(5 in)*because[36°] ≈ 60.68 in^2 (The area of each of 5 triangles is 1/2*base*height.)

However, the formula for the area based on side length gives

A = (5/4)*(6 in)^2*Tan[54°] ≈ 61.94 in^2

The area based on the radius of the circumscribing circle is

A = (5/2)*(5 in)^2*Sin[72°] ≈ 59.44 in^2

In short, the given "information" is inconsistent.

If the side length of a regular pentagon is 6 inches, the distance from a vertex to the center is about 5.1039 inches (not 5 inches). If the distance from the center to a vertex is 5 inches, the length of a side will be about 5.8779 inches (not 6 inches).