Final answer:
To solve for missing measures in parallelograms, use the geometric properties of vectors for resultant and difference, and apply proportions based on scale factors to find missing dimensions in scaled models. For area comparison, recognize that the area increases with the square of the scale factor when side lengths are multiplied.
Step-by-step explanation:
Finding Missing Measures in Parallelograms
To find the missing measures for parallelograms, there are different methods depending on the information provided. If vector quantities are given and you need to find the resultant or difference, you would construct a parallelogram where one vector originates from the tail of the other. The diagonals of this parallelogram represent the sum and difference of the vectors. For example, to measure the resultant R, you may use a ruler to find the length, and a protractor to determine the angle with respect to the horizontal.
In the context of geometry and scale factors, consider an example where a farmer wishes to calculate the length of the fourth side of a plot of land after measuring the first three sides. By using the properties of parallelograms, they can deduce both the length and direction of the missing side.
When dealing with area comparison between similar shapes like squares, if the side length of the larger square is twice that of the smaller square, then the area of the larger square will be four times greater, as area scales with the square of the length scale factor. This can be seen when Marta compares her two squares where the larger has a side length of 8 inches (double that of the smaller one), thus having an area four times as large.
To find a missing dimension when dealing with scales, you set up a proportion based on the scale factor. The scale is a comparison of the length in a model or drawing to the corresponding length on the actual object. For example, if the scale factor is 1/4":4' and the scale measurement is 12', you write a proportion to find the actual dimension.