Given:

Perimeter of square circumscribes a circle of radius ‘a’.

Side of square = Diameter of circle

Diameter of circle = 2 × radius

= 2a

So, Side of square = 2a

∵ Perimeter of square = 4 × side

∴ Perimeter of square = 4 × 2a

= 8a

Hence, the perimeter of the square is 8a.