Suppose you inscribe a square in a circle of radius r. Thus all four corners of the square lie on the circle. The area of that square is ?
well, the diagonal of the square is the diameter of the circle...
Suppose you inscribe a square in a circle of radius r. Thus all four corners of the square lie on the circle. The area of that square is ?
To find the area of the square inscribed in a circle, you can use the relationship between the side length of the square and the radius of the circle.
Let's denote the side length of the square as "s" and the radius of the circle as "r". Since the square is inscribed in the circle, each corner of the square touches the circumference of the circle.
When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. In this case, the diagonal of the square is two times the radius of the circle.
Using the Pythagorean theorem, we can find the relationship between the side length of the square and the radius of the circle:
s^2 + s^2 = (2r)^2
2s^2 = 4r^2
Dividing both sides of the equation by 2:
s^2 = 2r^2
To find the area of the square, we square the side length:
Area of the square = s^2 = (2r^2)
So, the area of the square inscribed in a circle of radius "r" is equal to 2 times the square of the radius (2r^2).