The perimeter (circumference) of a quarter-circle is one-fourth of the circumference of a circle. Furthermore, the length of each side of the equilateral triangles is equal to the radius of the circle. Can you find the perimeter now?
It is equal to the radius. To see why, extend the quarter-circle to produce a circle. Two of the sides of each equilateral triangle are radii, so each of the two sides have the same length as the length of the radius of the circle. Because all sides of an equilateral triangle are equal, the third side of each equilateral triangle also has the same length as the length of the radius of the circle.