The apothem is the distance from the center to the midpoint of one of the sides of a regular polygon. You can make a right triangle with the apothem, the line from the midpoint to the corner and the line from the center to the corner. An equilateral triangle has 60 degree angles (180/3). The right triangle has half of one of those angles so 30 degrees. Now we have a 30-60-90 triangle where the short leg is 5cm. The long leg, which is also half of one side of the triangle is thus [tex] 5\sqrt{3} [/tex]. A whole side of the triangle is [tex] 10\sqrt{3} [/tex]. Multiply that by 3 to get the perimeter of [tex] 30\sqrt{3} [/tex].
