Ah, well then what you have is a hexagonal pyramid. The surface area will be slightly more than the flat hexagon. If you want to match the exact size and shape of the umbrella, you can use direct measuremens from the umbrella.
In a hexagonal pyramid, the triangles are no longer equalateral but since you can measure it directly, the formula is much easier.
Surface Area = 6 * Triangle Area = 6 * (1 / 2 * B * H) = 3 * B * H
B = the length of one side of the hexigon
H = distance from the top of the umbrella to the mid point on a side measure on the surface (a flat hexagon reduces to sqrt(3) / 2 * B as previously shown)
However, you might want to plan for some waste so you don't come up short.
[EDIT] You must of posted while I was writing this. One more measurement would be useful if you want the exact surface area. Please measure from the top of the umbrella to the mid point on one of the sides. Otherwise, the surface area will be only the projection of the umbrella and you will come up short on material. A flat hexagon would be about 110 sq-ft.