what is the area of the largest square that can be cut from a circle of radius 1?

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sketch two perpendicular diameters and form your square.

let the side of the square be x
x^2 = 1^1 + 1^1 = 2

area of our square is x^2, so the area is 2 units^2

To find the area of the largest square that can be cut from a circle of radius 1, we can follow these steps:

Step 1: Start by visualizing the problem. Draw a circle with a radius of 1 on a graph paper or use a geometrical drawing software.

Step 2: The largest square that can be cut from a circle would have its four corners touching the circumference of the circle.

Step 3: Since the corners of the square are on the circumference of the circle, they will form a diagonal that is equal to the diameter of the circle (which is twice the radius).

Step 4: Therefore, the diagonal of the square is 2 times the radius, which is 2.

Step 5: We can use the Pythagorean theorem to find the side length of the square, which is the length of each of its four sides. According to the theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the two other sides. In this case, the diagonal is 2, so we have:

diagonal^2 = side^2 + side^2
2^2 = side^2 + side^2
4 = 2 * (side^2)
side^2 = 4 / 2
side^2 = 2

Step 6: Take the square root of both sides to find the length of one side of the square:

side = √2

Step 7: Finally, to find the area of the square, square the side length:

area = side^2
area = (√2)^2
area = 2 square units

Therefore, the area of the largest square that can be cut from a circle of radius 1 is 2 square units.