Easy-peasy.

Find the width from face to face, and multiply that by 0.86, then multiply the two together to get your area.

For example, if your hex is nominally 25 miles wide from face to face, its area will be 25 * (25 * 0.86 = 21.5) = 537.5 square miles.

The illustration to the right displays how this is so; you will note that triangles A and a, and B and b are the same size. Move AB to ab and we get a rectangle of dimensions 1 x 0.86 — simple as that.