Final answer:
To find the area of a parallelogram using only the area formula for a rectangle, one must deconstruct the parallelogram into a rectangle, apply the formula A = lw, and compare the areas through a ratio if necessary. Proportions are essential for comparing the changes in area when dimensions are scaled.
Step-by-step explanation:
The process of finding the area of a parallelogram by breaking it down into a rectangle is to first deconstruct the parallelogram into a rectilinear shape where the formula for the area of a rectangle (A = lw) can be applied. To do this, you can cut a parallelogram into two pieces by slicing along a diagonal, then rearrange those two pieces to form a rectangle or a square. Consequently, if the parallelogram has a base b and a height h, the area can still be calculated using the area formula A = bh, which represents the rectangle's length and width in the context of a parallelogram.
Comparing two areas, the relationship between them can be articulated through a ratio. For instance, if you have two squares, one with side length a and the other with side length 2a, their areas would be a^2 and (2a)^2 respectively. The ratio of the larger area to the smaller area is 4:1 since (2a)^2 = 4a^2, which is four times a^2.
When calculating changes in area or comparing different spaces, understanding how dimensions scale with size is crucial. Proportions and scale can help in calculations of areas and distances for comparison.