r=1, therefore each side of the hexagon is 2. You can also split the hexagon into 2 half and you have two trapezoids with a base of 2 and 4.
You can also determine the size of each of the angle on the trapezoid by using the formula;
[(number of sides -2)180]/6 = [(6-2)180] = (4*180)/6 = 720/6 = 120
You need to know this so you can calculate the height of the trapezoid. Draw a line from the corner of the smaller base straight down to form a 90 degree angle with the larger base. This creates a 30-60-90 triangle because you have 90 degree angle where you drew the line down and a 60 degree angle where you split the trapezoid in two. From there you can deduce that the other angle must be 30 degrees.
So you have a 30-60-90 triangle with a hypotenuse of 2. 30-60-90 triangles sides are in the ratio x : x[sqrt(3)] : 2x, from smallest side to largest side. You hypotenuse is 2 so the smallest side of the triangle must be 1 and the middle length side must be 1[sqrt(3)]. Thus, the height of the trapezoid is sqrt(3).
So, formula for the area of a trapezoid is;
[(base 1 +base 2)*height]/2, so
[(4+2)*sqrt(3)]/2 = (6sqrt(3))/2
But we have two trapezoids in the circle so the area of the hexagon is;
[(6sqrt(3))/2]*2 = 6sqrt(3)
