Question

A circle is circumscribed about a square. If the sides of the square are 4, what is the exact circumference of the circle?

Answer 1

Since we know the sides of the square which are L = 4 units, then by Pythagorean theorem we can find the diagonal of the square which is
d = ((4 ^ 2) + (4 ^ 2)) ^ (1/2) = 5.66
Then, since the diagonal of the square is also the diameter of the circle, then the circumference of the circle will be the product of Pi per diameter:
C = pi * d = pi * 5.66 = 17.77 Units