It looks straight forward to me. I assume, of course that you mean a regular dodecahedron since otherwise this is impossible. If the distance between opposite vertices is 2, then the distance from center to each vertex is 1. So you have 12 isosceles triangle with side lengths 1 and vertex angle 360/12= 30 degrees. Dividing each isosceles triangle in half gives 24 right triangles with hypotenuse of length 1 and angle 30 degrees. Can you find the lengths of the legs, so the area of each right triangle, and the multiply by 24?