The midpoints of a regular hexagon are connected to form a smaller hexagon. The small hexagon has perimeter $2\sqrt{3}.$ What is the perimeter of the large hexagon

Respuesta :

The perimeter of the large hexagon is equal to 12 units.

Explanation:

Given,

The perimeter of small hexagon = [tex]2\sqrt{3}[/tex]

To find, the perimeter of the large hexagon = ?

We know that,

The perimeter of the large hexagon

[tex]= \dfrac{6}{\sqrt{3}}[/tex] × The perimeter of small hexagon

= [tex]\dfrac{6}{\sqrt{3}} \times 2\sqrt{3}[/tex]

= 6 × 2

= 12 units

∴ The perimeter of the large hexagon = 12 units

Thus, the perimeter of the large hexagon is equal to 12 units.

Answer:

4

Explanation:

we can set up a 120,30,30 isosceles triangle than divide it into two 30 60 90 triangles then 2 rt 3 divide it by 12 (the hexagon and the two triangle) then we get 1/6 rt 3 after that we get 1/3 as the side length but since we divide by 2 we need to multiply by two thus getting us 2/3 but to get the perimeter, we need to multiply by 6 and our final answer is 4