Final answer:
To find the measure of side NO in similar quadrilaterals, we would normally use ratios to compare corresponding sides. However, without specific measures for IJKL, we cannot calculate NO. An example with squares illustrates how the area of similar figures with a scale factor of 2 would be 4 times greater.
Step-by-step explanation:
The problem you've given is about the similarity of quadrilaterals and understanding how their proportional sides relate to one another. In the context of similar geometric figures, we know that the ratio of corresponding sides is consistent. Although the actual dimensions for quadrilaterals IJKL and MNOP are not given, the basic principle we would use is to set up a proportion using the sides of IJKL that correspond to sides MN and OP of the similar quadrilateral.
For example, if we knew side IJ corresponded to side MN and side KL corresponded to side OP, and if we had the measures of IJ and KL, we could create a proportion such as IJ/MN = KL/OP. From this proportion, we could then solve for the unknown measurement of side NO by cross-multiplying and dividing as necessary.
In terms of the problems you've cited, for example, if Marta has a square with side length of 4 inches and a similar square with dimensions twice the size, the side length of the larger square would be 8 inches. The area of the larger square would be 64 square inches (since area = side length squared) and the area of the smaller square would be 16 square inches. Hence, the area of the larger square is four times greater than that of the smaller square (since 64 is four times 16).