Will mark what is the ratio of the area of the drawing to that of the actual bedroom?

The answer is b.
Since the area of a square is a side length squared, if one side length is multiplied by 2, the area is multiplied by 4. If the side length is multiplied by 4, the area increases by 16 times, etc. In the question, the side lengths in the actual bedroom are double the drawing, so the area will be multiplied by 2^2, which is 4. So, if the side length ratio is 1/2, the area ratio will be 1^2 / 2^2. That simplifies to 1/4.