Area

A=1/4√(5(5+2√5))a^2 if a is a side

Thanks,  Landry.......here's another formula....if we know the side length

We have 5 equal isoceles triangles.......each with an apex angle of 72°

If we know the side length, the height of each triangle can be found, thusly:

tan (36) = (1/2)s / h

h = s / [2 tan 36]  =  (1/2)s*cot36

So....the area of one triangle =

(1/2)s * (1/2)s * cot 36  =

(1/4)s^2 * cot(36)

So....the total area =

(5/4)s^2*cot(36)  =

(5/4)s^2 * tan(54)