Question

A hexagonal prism 6 ft tall with a regular base measuring 9 ft on each edge and an apothem of length 7.8 ft. How do I get the lateral and total surface area, rounding it to the nearest tenth if necessary?

Answer 1

Given:

Hexagonal Prism dimensions: 

Altitude = 6 ft
Regular base;
side = 9 ft
apothem = 7.8 ft

The formula for the lateral surface area of a prism is

LA = P * h

where 
LA is the lateral surface area
P is the perimeter of the base
h is the height of the prism

LA = (9 ft * 6 sides) * 6 ft
LA = 324 ft^2

The formula for total surface area is 

TA = (P * h) + 2(Ab) 

where 
TA is the total surface area
Ab = Area of the base

Ab = a * P / 2
Ab = 7.8 ft * (9ft * 6) / 2
Ab = 210.6 ft^2

TA = 324 + 2(210.6)
TA = 745.2 ft^2
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