The formula for the surface area of a regular pyramid is SA = B + 1/2Pl.
B is equal to the area of the base. To find the area of a regular hexagon, use the formula 1/2aP.
To find the apothem, divide one side length by two to get 3. The perimeter is 6 · 6 = 36 = P
1/2 · 3 · 36 = 54 = B
Now that we found the area of the base, let's move on to the second part of the equation. l is the slant height of one lateral face of the regular pyramid. Use the Pythagorean Theorem to find such side.
a² + b² = c²
3² + 8² = c²
9 + 64 = c²
√73 = c = l
Putting it all together...
SA = 54 + 1/2(36)(√73)
SA = 54 + 18√73
Alternatively: 207.79 approx.
