Question

How do you find the lateral surface area of a hexagonal prism with height $10m$ and base edge $4m$ ?

Answer 1

Hint:
A hexagonal prism consists of $8$ faces, with top and bottom as a hexagon and the remaining faces as a rectangle. The lateral surface area of this prism will be the area of all the faces except the top and bottom hexagons. Find the lateral area using this information.

Complete step by step solution:
Here in this problem, we have a hexagonal prism with the height of $10m$ and base edge of $4m$ . And we need to find the lateral surface area of this prism.
Using the given information in the question, let’s construct a rough diagram for a better understanding

Before starting with the solution we must understand the fundamentals of the lateral surface area of the prism. A hexagonal prism is a three-dimensional shape having a base and top of a regular hexagon. The remaining side faces are in the form of rectangles. When a prism has its bases facing up and down, the lateral area is the area of the vertical faces. (For a rectangular prism, any pair of opposite faces can be bases.) The lateral area of a right prism can be calculated by multiplying the perimeter of the base by the height of the prism.
$ \Rightarrow $ The lateral surface area of prism $ = $ Combined area of rectangular faces
Therefore,
$ \Rightarrow $ The lateral surface area of the prism $ = 6 \times \left( {{\text{Area of rectangle face}}} \right) = 6 \times {\text{Base Edge}} \times {\text{Height}}$
On substituting the required value, we get:
$ \Rightarrow $ The lateral surface area of the prism $ = 6 \times {\text{Base Edge}} \times {\text{Height}} = 6 \times 4 \times 10{\text{ }}{{\text{m}}^2}$
After solving the product of the length of the base edge and height, we get:
$ \Rightarrow $ The lateral surface area of the prism $ = 240{\text{ }}{m^2}$

Thus, we get the required lateral surface area of the hexagonal prism is $240{\text{ }}{m^2}$

Note:
In mensuration, the understanding of the formula to be used for solving plays a crucial part in solving problems. Drawing a rough diagram to represent the given information also helps in understanding the question clearly. An alternative approach can be to find the area of one rectangular face separately and then find six times of that area to find the required answer.