Question

find the area of a hexagon inscribed in a circle of radius r
in terms of r

Answer 1

Step 1: Use what we know:
Here, we can easily tell that the long diagonal is the diameter of the circle which is 2r. 2r is also equal to 2 times the side length of the hexagon. This means that the side length of the hexagon is r. 

Step 2: Find the area:
The area of an equilateral triangle is   $\frac{a^2 \sqrt{3} }{4}$ and so the area is $\frac{3r^2 \sqrt{3} }{2}$