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?

Question

Mathematics

Matteo Golden

31 March, 17:50

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?

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Answers (1)

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Carly · 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