Square ABCD is incribed in Circle O. If the side of the square is 2 find the area of Circle O.

a. pi
b. 2 pi
c. 4 pi
d. 8 pi
e. 16 pi

please answer and explain

Hint: If you have a side of the square, then you can get the diagonal from one corner of the square to the other.

A=pi r^2

= pi 2^2

= 4 pi

answer c

am i right?

the area of the square is 2^2, but the diameter of the circle is the diagonal of the square.

Since the side is 2, the diagonal is 2√2
The radius is half the diameter, or r = √2

the area of the circle is thus pi r^2 = 2pi

To find the area of Circle O, we need to determine the radius of the circle. Since Square ABCD is inscribed in Circle O, the diagonal of the square will be equal to the diameter of the circle.

The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the square is the hypotenuse, and the length of one side of the square is one of the other two sides. Let's call the diagonal of the square D.

Using the Pythagorean theorem, we have:

D^2 = (2)^2 + (2)^2
D^2 = 4 + 4
D^2 = 8
D = √8

The diameter of Circle O is equal to √8, and therefore, the radius (r) of Circle O is half of the diameter:

r = (√8)/2 = √2

Now, we can calculate the area of Circle O using the formula for the area of a circle:

Area = πr^2

Substituting the value of the radius into the formula:

Area = π(√2)^2
Area = π * 2
Area = 2π

Therefore, the area of Circle O is 2π.

The correct answer is (b) 2π.