# Find the circumference of a circle circumscribed about a square and the area

June 30, 2021 | education

| **Find the circumference of a circle circumscribed about a square and the area of a circle inscribed in the same square if the side of the square is 20 cm.**

From the condition, we know that the circle is circumscribed about a square, and we are also given the value of the side of the square – 20 cm.

To find the circumference of a circle, you must first of all find its radius using the following formula.

R = a / √2.

Substitute and calculate: R = 20 / √2 = 10√2 cm.

Circumference:

l = 2πR = 2 * π * 10√2 = 20π√2 cm circumcircle length.

Find the radius of the inscribed circle:

r = a / 2 = 20/2 = 10 cm.

We are looking for the area of the circle by the formula:

S = πR ^ 2;

S = π * 10 ^ 2 = 3.14 * 100 = 314 cm2 inscribed area.

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