Answer:
Step-by-step explanation:
a hexagonal prism is made up of two bases that are hexagons and six faces that are rectangles.
Lateral surface area, LA = Perimeter × height
Perimeter = number of sides × length of each side
Perimeter, P = 6 × 10 = 60
LA = 60 × 12 = 720 units squared
Area of each base, B = 1/2a × perimeter
Where
a = apotherm
We would determine the length of the apotherm of each base of the prism by applying the formula,
a = s/[2tan(180/n)]
Where
s = length of each side = 10
n = 6 sides
a = 10/[2tan(180/6) = 10/[2tan30)
a = 8.66
B = 1/2 × 8.66 × 60 = 259.8
Total surface area = LA + 2B
Total surface area = 720 + 2 × 259.8 = 1239.6 units squared
