To find the ratio of the areas of the squares, we need to find the dimensions of the squares EFGH and ABCD.
Let's assume that the side length of square ABCD is "a". Since square ABCD is inscribed in a circle, the diagonal of square ABCD is equal to the diameter of the circle. The diagonal of a square can be found using the Pythagorean theorem:
Diagonal^2 = Side^2 + Side^2
D^2 = a^2 + a^2
D^2 = 2a^2
D = √(2a^2) = √2 * a
Now, let's consider the semi-circle formed by folding the circle. The diameter of the semi-circle is equal to the diagonal of square ABCD, which we found to be √2 * a. The radius of the semi-circle is half of the diameter, so:
Radius = (√2 * a) / 2 = √2 * a / 2
The diagonal of the square EFGH is equal to the diameter of the semi-circle, so it is also √2 * a. Therefore, the side length of square EFGH is:
Side length of EFGH = (√2 * a) / √2 = a
Now let's find the area of the two squares:
Area of square ABCD = a^2
Area of square EFGH = (a)^2 = a^2
The ratio of the area of square EFGH to the area of square ABCD is:
(a^2) / (a^2) = 1
Therefore, the ratio of the area of square EFGH to the area of square ABCD is 1:1.