Question

The midpoints of a regular hexagon are connected to form a smaller hexagon. The small hexagon has perimeter 2sqrt3. What is the perimeter of the large hexagon?

Answer 1

Answer:

4

Step-by-step explanation:

x - length of side of larger hexagon

y - length of side of smaller hexagon

We know that,

x/y = $\sqrt{3} /2$

y = $2x/\sqrt{3}$

Hence,

perimeter of             = $(2/\sqrt{3})$ * perimeter of smaller hexagon

larger hexagon

                                 = $(2/\sqrt{3})*2\sqrt{3} \\= 4$