The ratio of the area of a square to that of the square drawn on its diagonal can be determined by understanding the relationship between the sides of a square and its diagonal.

Understanding the relationship between the sides and diagonal of a square:
- In a square, all sides are equal in length.
- The diagonal of a square is a line segment that connects two opposite vertices.
- The diagonal of a square divides it into two congruent right triangles.

Explaining the solution:
To find the ratio of the areas, we can assume the length of one side of the square as 's'.
- The area of the square is given by A = s^2.
- The length of the diagonal of the square can be found using the Pythagorean theorem, as the diagonal forms the hypotenuse of the right triangle.
- The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- In this case, the hypotenuse is the diagonal, and the other two sides are the sides of the square.
- Applying the Pythagorean theorem, we have d^2 = s^2 + s^2 = 2s^2.
- Taking the square root of both sides, we get d = sqrt(2s^2) = sqrt(2)s.

Calculating the ratio of the areas:
- The area of the square drawn on the diagonal is given by A_d = (sqrt(2)s)^2 = 2s^2.
- Dividing the area of the square by the area of the square drawn on the diagonal, we get A/A_d = s^2 / 2s^2 = 1/2.

Therefore, the ratio of the area of the square to that of the square drawn on its diagonal is 1:2, which corresponds to option 'C'.