Question

what is the perimeter of a square circumscribe a circle of radius a cm

Answer 1

When a square circumscribes a circle, the radius of the circle is half the length of the square.

Therefore if the radius of the circumscribed circle is a, the diameter will be 2a. It is this diameter that is equal to the length of the square.

Therefore the length of the square is 2a  cm.

The area of a square is 4 × length

                    =  4 × 2a cm 

                    = 8a cm

Answer 2

here is ur answer:

radius = a

diameter = 2a

diameter of circle = diagonal of square

$2a = \sqrt{2} \times side \\ \\ \frac{2a}{ \sqrt{2} } = side \\ \\ side = \sqrt{2} a$

now,

perimeter of square = 4 × side

perimeter of square = 4 × √2a

perimeter of square = 4√2a

hope it helps you!