Find the lateral area and surface area of a regular hexagonal right prism is the base edges are 10 and the height is 12.

Round your answer to the nearest tenth.

LA = units squared

SA = units squared

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