The surface area of the solid is 487.2ft²
What is surface area of prism?
The surface area of a prism is the sum of the areas of its lateral faces and the two bases.
Generally, the surface area of prism is expressed as ;
SA = 2B + ph
B = base area and p is the perimeter of the base and h is the height of the prism.
The base of the prism is pentagon
area of polygon = (p × a)/2
where P is the perimeter
perimeter = 5 × 8.12 = 40.6
a is the apothem
apothem = 7
area = 40.6 × 7/2
= 142.1ft²
SA = 2 × 142.1 + 40.6 × 5
= 284.2 + 203
= 487.2ft²
Therefore the surface area of the solid is 487.2ft²