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.

3 Answers | Add Yours

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The side of the square is inscribed in a circle  is given to be 2sqrt2.

So the diagonal of the square = sqrt{2*square of the side of the square } = sqrt{2* (2*sqrt2)^2} =  sqrt{16} = 4.

Therefore the diagonal of the square is 4.

The diagonal of the square must be the diameter of the square inscribed in the circle.

Therefore the radius of the circle =  diameter of the circle/2 = 4/2 = 2.

Therefore the circumference of the circle = 2pi*radius = 2pi*2 = 4pi.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know that the diagonal of the inscribed square is the diameter of the circle.

We'll determine the diagonal applying the Pythagorean theorem.

The diagonal is the hypothenuse of the both right angled triangles formed by it.

We'll note the hypothenuse by a:

a^2 = (2sqrt2)^2 + (2sqrt2)^2

a^2 = 8 + 8

a^2 = 16

a = 4

We'll consider only the positive value of the hypothenuse.

The circumference of a circle is:

C = 2pi*r, but 2r = a = diameter

C = a*pi

C = 4pi

We’ve answered 318,935 questions. We can answer yours, too.

Ask a question