Find the total surface area of a hexagonal prism 6ft tall with a regular base measuring 9ft on each and an apothem of length 7.8ft

Answer 1

The hexagon is made up 6 equilateral triangles with sides of 9 ft
Area of one of them = (1/2)(9)(9)sin60°
= (81/2)(√3/2) = 81√3/4

area of whole hexagon
= 6(81√3/4) = 243√3/2

area of whole hexagonal prism
= 2(243√3/2) + 6(9)(6)
= (243√3 + 324) ft^2

your value for the apothem of 7.8 is not needed.
Btw, the exact value of the apothem is 9sin60°
= 9√3/2