Question

Find the perimeter of a regular hexagon with each side measuring 8 meters.

Answer 1

Hint: We should know that the sum of all sides of a polygon is equal to the perimeter of the polygon. We should also know that all the sides of a regular polygon are equal. We know that a hexagon is a polygon of six sides. A regular hexagon will have all six sides as equal. Let us assume the length of a side of a hexagon is equal to x. Then we will get the length of all the sides of the hexagon is equal to x m. Now we have to find the perimeter of the hexagon whose side is equal to x. Let us assume this equation as equation (1). Now we have to substitute the value of x as equal to 8, to find the perimeter of the hexagon whose length is equal to 8 meters.

Complete step-by-step answer:
Before solving the question, we should know that the sum of all sides of a polygon is equal to the perimeter of the polygon. We should also know that all the sides of a regular polygon are equal.
We know that a hexagon is a polygon of six sides. A regular hexagon will have all six sides as equal. Let us assume the length of a side of a hexagon is equal to x. Then we will get the length of all the sides of the hexagon is equal to x m.

Let us assume the perimeter of the hexagon is equal to p.
From the above diagram, it is clear that
$$\begin{array}{rl}& \Rightarrow p=AB+BC+CD+DE+EF+FA\\ & \Rightarrow p=x+x+x+x+x+x\\ & \Rightarrow p=6x......(1)\end{array}$$
From equation (1), it is clear that if the measure of the length of the side of the hexagon is equal to x then the perimeter of the hexagon is equal to 6x.
From the question, it was given that the length of the side of a hexagon is equal to 8 m.
Now we have to find the perimeter of the hexagon.
So, we have to substitute $$x=8$$ in equation (1).
$$\begin{array}{rl}& \Rightarrow p=6(8)\\ & \Rightarrow p=48.........(2)\end{array}$$
From equation (2), it is clear that the perimeter of a regular hexagon with each side measuring 8 meters is equal to 48 meters.

Note: Students should know the perfect definition of perimeter. If a student did not have a clear view on the concept of perimeter, then it is not possible to do this question. So, a clear view is required to solve this problem. Students should be careful at calculation part of this question. If a small mistake is made, then it is not possible to get a correct final answer. So, one should do the calculation part in a perfect manner.