The apothem, a, of a regular pentagon is the distance from the center of the pentagon to the midpoint of an edge.
Trigonometry can be used to show that a = (s/2) /tan(pi/10), where s is the length of a side. This is an exact result.
The area, A, of a regular pentagon is A = 5 a s/2
The volume, V, of a pyramid is V = (1/3) A h, where h is the height.
The height can be obtained from the slant height, SH, by SH2 = h2 + a2
The surface area, SA, is given by A + 5 (SH a /2)
Taken together, these formulas give an exact answer to the questions.
Numerical results can be worked out:
a = (s/2) /.7265425 = 7.5701004
A = 5 a s/2 = 208.17776
h = sqrt(SH2 - a2) = 9.9470388
V = (1/3) h A = 690.25022
With the numerical results for a, S and h, a value for the surface area can also be worked out.