A square is inscribed in a circle, side of the square is 2*squareroot2. What is the circumference of the circle in terms of pi.

Expert Answers

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Given that the side of the square is 2sqrt2.

Then, we know that the diagonal pf the square is the diagonal of the circle.

Let us calculate.

The diagonal = sqrt(side^2 + side^2)

                     = sqrt( 2sqrt2)^2 + (2sqrt2)^2

                    = sqrt ( 8 +8) = sqrt 16 = 4

Then, the diagonal of the circle is 4 units.

Now we need to find the circumference is the circle.

We know that the circumference is given by:

C = 2*r *pi

But r = diagonal/2 = 4/2 = 2

==> C = 2*2 * pi = 4pi

Then, the circumference of the circle is 4*pi units.

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