Write an equation that relates the number of parallelograms in the figure (n), to the perimeter of the figure (P).
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The top and bottom = 5 each and the sides = 4 each in each figure.
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To find an equation that relates the number of parallelograms in the figure (n) to the perimeter of the figure (P), we need to understand the pattern and relationship between these two variables.
Let's analyze the given figure:
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5 5
From the figure, we can see that there are three rows of parallelograms stacked on top of each other. Each row has a total length and perimeter of 5 units.
In the first row, there is only one parallelogram, and each side of the parallelogram has a length of 4 units. Therefore, the first row contributes 4 units to the total perimeter.
In the second row, there are two parallelograms, each with a side length of 4 units. Hence, the second row contributes 8 units to the total perimeter.
Finally, in the third row, there are three parallelograms, each with a side length of 4 units. So, the third row contributes 12 units to the total perimeter.
To summarize, each row contributes a number to the total perimeter equal to the number of parallelograms in that row multiplied by the length of each side of the parallelogram.
Based on this pattern, we can write the equation relating the number of parallelograms (n) and the perimeter (P):
P = 4n + 8 + 12
This equation accounts for the contribution from each row and the additional 8 units and 12 units from the first row's sides.