the endpoints of one side of a regular hexagon are (-9,-4) and (-1,2). the perimeter of the hexagon is..?

Question

the endpoints of one side of a regular hexagon are (-9,-4) and (-1,2). the perimeter of the hexagon is..?

Answer 1

When we refer to a polygon as "regular" we mean that the sides are all the same length. To find the perimeter of a polygon, we add up all of the side lengths. The problem here is that we don't know the side lengths, only the endpoints of one of the sides. Thankfully, we can use the distance formula to find the length of the side. The distance formula is as follow:

√(x₂-x₁)²-(y₂-y₁)²

Now we just plug in the given points:

√(-1-(-9))²-(2-(-4)² = √(1+9)²-(2+4)² = √(10)²-(6)²= √(100-36) = √64 = 8

So now we know that all of the side lengths of our hexagon is 8 units! Now remember a hexagon has 6 sides. So we can do one of two things to find the perimeter. Either add 8 to itself 6 times or just multiply 8 times 6, you'll get the same answer no matter which method you use. I will keep it simple and just multiply by six:

perimeter = 8 * 6 = 48 units²

There you have it! I hope this explanation was thorough and answered all your questions! If you have any questions please don't hesitate to reach out! :)