A regular hexagon is made from equilateral triangle by cutting along the dotted lines and removing the three smaller triangles. if triangle has a perimeter of 18, what is the perimeter of hexagon?

Where are the dotted lines?

To find the perimeter of the hexagon, we first need to determine the side length of the equilateral triangle.

We know that the perimeter of the equilateral triangle is 18, and since all three sides are equal, each side of the equilateral triangle has a length of:

18 / 3 = 6

Now, to find the perimeter of the hexagon, we need to consider that the hexagon is made up of six equilateral triangles, each with a side length of 6.

The perimeter of the hexagon is then:

Perimeter = 6 * side length of equilateral triangle
Perimeter = 6 * 6
Perimeter = 36

Therefore, the perimeter of the hexagon is 36.

To solve this problem, we need to understand the relationship between the equilateral triangle and the regular hexagon.

An equilateral triangle has three equal sides. Let's say each side of the triangle has a length of "a". So, the perimeter of the equilateral triangle is given as 3a.

Now, when we cut along the dotted lines and remove the smaller triangles from the equilateral triangle, we are essentially left with a regular hexagon.

A regular hexagon is a polygon with six equal sides. Since the sides of the hexagon are the same as the sides of the equilateral triangle, each side of the hexagon also has a length of "a".

Now, to find the perimeter of the hexagon, we can simply multiply the length of one side (a) by the number of sides in a hexagon (6). Therefore, the perimeter of the hexagon is 6a.

Since we are given that the perimeter of the equilateral triangle is 18, we have 3a = 18. Solving for "a", we divide both sides of the equation by 3: a = 18/3 = 6.

Now that we know the length of one side of both the equilateral triangle and the hexagon (a = 6), we can find the perimeter of the hexagon by multiplying the length of one side (6) by the number of sides in a hexagon (6).

Perimeter of hexagon = 6a = 6 * 6 = 36.

Therefore, the perimeter of the hexagon is 36.

If an equilateral triangle has a perimeter of 18,the length of each side of the triangle is six(18/3=6). Therefore, the perimeter of the hexagon is thirty-six(6x6=36).

If a straight line is drawn from the center to each vertex, six congruent equilateral triangles are formed. The perimeter of the hexagon is equal to the sum of the six sides(36).