Make it bigger

Relevant wiki: Regular Polygons - Area

A regular hexagon with side length 8 has an area of $96\sqrt{3}$ . To calculate its area, first divide it into six identical equilateral triangles . Now, let's first find the area of one triangle. The area of an equilateral triangle is $\frac{s^{2}\sqrt{3}}{4}$ , and we plug in 8 for $s$ to get the area $16\sqrt{3}$ . Because a regular hexagon is made of 6 equilateral triangles, we get that the area of the hexagon is $6 \times 16\sqrt{3} = 96\sqrt{3}$ .

It is 4 times as big as the hexagon we would like to construct. So why would you not just divide 8 by 4?

Well, see the $s^{2}$ in the area formula? If you divide the side length or an equilateral triangle by 4, we will end up with a triangle $\frac{1}{16}$ as big since $(\frac{1}{4})^{2} = \frac{1}{16}$ . So, in order to get a hexagon $\frac{1}{4}$ as big, we need to find the square root of $\frac{1}{4}$ , which is ${1}{2}$ in this case. That means the side length we want is $\frac{1}{2}$ as big. Yippees! Our answer is $\boxed{1:2}$ .