# Find the length of a circle circumscribed about a square with side 4.

March 31, 2021 | education

| Since a circle is circumscribed around the square, its center is the intersection point of the diagonals of the square, and the diagonal itself is the diameter of the circumscribed circle.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + AC ^ 2 = 16 + 16 = 32.

AC = 4 * √2 cm.

Then R = AC / 2 = 4 * √2 / 2 = 2 * √2 cm.

Determine the length of the circle.

L = 2 * π * R = 2 * π * 2 √2 = π * 4 * √2 cm.

Answer: The circumference is π * 4 * √2 cm.

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