Question

What is the area of a regular hexagon with a distance from its center to a vertex of 1 cm? (Hint: A regular hexagon can be divided into six equilateral triangles.)

Answer 1

The area of a regular polygon given the radius is:
$area= \frac{r^2*n*sin(\frac{360}{n})}{2}$
given:
r=1
n=6
Then the area will be:
$area= \frac{1^2*6*sin(\frac{360}{6})}{2}$
area=$\frac{3 \sqrt3}{2}$ cm²