If it is
meant to be solved as an area, what I would do is set it up as a grid and take it from there (combining shapes to become regular shape and then measuring the are of those), because plain old getting it from the picture is very improbable, unless you have a program to measure the lines, to get the perimeter and multiplying that by itself. Other than that, I have no idea. To have an equation for a shape 'without a name', is different. I would help you, but I'm still in high school, and haven't taken calculus, which I hear is need to take on to these 'without a name' shapes.
If you wanted to find the area of a three dimension Icosahedron, I can help you.
Number of vertices: v
Number of edges: e
Number of faces: f
Edge: a
Radius of circumscribed sphere: R
Radius of inscribed sphere: r
Surface area: S
Volume: V
Dihedral angle between faces: delta (in degrees)
v = 12, e = 30, f = 20
a = (sqrt[50-10 sqrt(5)]/5)R
r = (sqrt[75+30 sqrt(5)]/15)R
R = (sqrt[10+2 sqrt(5)]/4)a
r = (sqrt[42+18 sqrt(5)]/12)a
S = 5 sqrt(3)a2
V = (5[3+sqrt(5)]/12)a3
delta = arccos(-sqrt[5]/3) = 138o 11'
http://mathforum.org/dr.math/faq/for...ages/icosa.gif