SOLUTION: The sides of a square are 8 cm. find the circumference of the circumscribed circle.

Draw a diagonal of the square (in green):



That green diagonal is a diameter of the circle, and its length can
be calculated using the Pythagorean theorm on the right triangle which
is the lower half of that square.

a² + b² = c²
8² + 8² = c²
64 + 64 = c²
    128 = c²
   √128 = c
  √64·2 = c
    8√2 = c

So the diameter of the circle is 8√2cm

The formula for the circumference of a circle is

C = pd where d is the diameter.

C = p·8√2

C = 8p√2.

That's approximately 35.543 cm.


Edwin