SOLUTION: I have a problem with a square inside a circle. The length of the square is 2 and the width of the square is 2. what is the area of the circle and how do you figure this out? Thank

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Question 322750: I have a problem with a square inside a circle. The length of the square is 2 and the width of the square is 2. what is the area of the circle and how do you figure this out? Thanks in advance.
Found 2 solutions by Alan3354, jessica43:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
I have a problem with a square inside a circle. The length of the square is 2 and the width of the square is 2. what is the area of the circle and how do you figure this out?
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The diameter is the diagonal of the square, d = 2sqrt(2).
The radius is half that, r = sqrt(2)

=~ 6.28 sq units

Answer by jessica43(140) (Show Source):
You can put this solution on YOUR website!
To solve this problem you are going to need to use the Pythagorean theorem which is: a^2 + b^2 = c^2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. This formula can only be used for right triangle.
So you know that the length and width of the square are each two. In your picture, draw in one of the diagonals of the square, so now it is split into 2 right triangles. You will also notice that this diagonal line of the square is also the diameter of the circle. So we need to find the length of this line by using the pythagorean theorem.
We know two of the sides of the triangle are 2, so we can find the third.
a^2 + b^2 = c^2
(2^2) + (2^2) = c^2
4 + 4 = c^2
8 = c^2 (next take the sqrt of each side)
c = sqrt(8) or 2.828
So the diameter of the circle is about 2.828 and the radius is half of that, or about 1.414. Now we can use the area of a circle equation.
A = π * r^2 (r = radius)
A = π * (1.414)^2
A = π * 2
So the area of the circle is 2π or about 6.28.