Surface Area and Volume of a Hexagonal Prism

A hexagonal prism is a three-dimensional shape with six identical triangular faces. It has a hexagonal base and a rectangular lateral surface. In this article, we will explore the surface area and volume of a hexagonal prism.

The first step in finding the surface area and volume of a hexagonal prism is to find its lateral area (LA). The lateral area is the sum of the areas of all the lateral faces. According to Theorem 87, the lateral area of a right prism with altitude h and perimeter p is given by the following equation:

LA = ph

In our case, the perimeter of the hexagonal base is given as 3 + 4 + 5 ft, or 12 ft. Since the altitude of the prism is given as 2 ft, we can plug these values into the equation to find the lateral area:

LA = 12 x 2

= 24

The next step is to find the total area (TA) of the hexagonal prism. According to Theorem 88, the total area of a right prism with lateral area LA and base area B is given by the following equation:

TA = LA + B

Since we already found the lateral area, we can plug it into this equation along with the base area. However, we need to find the base area first.

The base area of a hexagonal prism is the sum of the areas of its triangular faces. Since there are six identical triangular faces, each with an altitude of 2 ft and a base of (3 + 4) ft = 7 ft, we can find the base area by multiplying the base by the altitude:

B = 6 x (7 x 2)

= 84

Now that we have the lateral area and base area, we can find the total area:

TA = LA + B

= 24 + 84

= 108

Finally, we need to find the volume (V) of the hexagonal prism. According to Theorem 89, the volume of a right prism with base area B and altitude h is given by the following equation:

V = Bh

Plugging in the values, we get:

V = 84 x 2

= 168 cubic inches

In conclusion, the surface area of the hexagonal prism is 108 square feet and its volume is 168 cubic inches.

Surface area and volume of a hexagonal prism