Final answer:
To convert a parallelogram into an equivalent rectangle, maintain the same base and height to ensure the area remains unchanged. This application of Euclid's geometrical principles guarantees the rectangle's area matches that of the original parallelogram.
Step-by-step explanation:
To convert a parallelogram into a rectangle with the same base and area, we can apply the principles from Euclid's propositions that pertain to areas and parallelogram properties. By constructing a rectangle that has the same base and height as the parallelogram, we ensure that the areas are identical, since the area of a parallelogram is given by the product of its base and height, and the same holds true for a rectangle. Consequently, if we have a parallelogram with a base 'b' and height 'h', to create an equivalent rectangle, we simply need to use one of the sides of the parallelogram as the base and then draw perpendicular lines from the ends of this base to the opposite side, thus maintaining the same base 'b' and height 'h' as the original parallelogram.
For example, let's consider the problem where Marta has a square with a side length of 4 inches; a similar square has dimensions that are twice the first square. The area of the larger square will be 4 times the area of the smaller square because the area is proportional to the square of the sides' lengths. In this example, the sides of the larger square are twice as long, thus (2x)^2 = 4x^2, which means the area is 4 times greater.