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Table:
Number of Hexagons n | Perimeter p |
---|---|
1 | 6 |
2 | 10 |
3 | 14 |
Words: See solution.
Equation: P=4n+2
Graph:
Let's take a look at the given figures.
Let's make a table that shows the perimeter of the figures p depending the number of hexagons n.
Number of Hexagons n | Perimeter p |
---|---|
1 | 6 |
2 | 10 |
3 | 14 |
Next, we will interpret this table.
The pattern we see is that the perimeter of the figures increases by 4, as the number of hexagons increases by 1. We can use this to write an equation that represents the perimeter of the figures.
Number of Hexagons n | P=4n | Perimeter Found by the Formula | Actual Perimeter |
---|---|---|---|
1 | P=4( 1) | 4 | 6 |
2 | P=4( 2) | 8 | 10 |
3 | P=4( 3) | 12 | 14 |
The perimeter found by the incomplete formula is always 2 less than the actual perimeter. Therefore, we can complete our formula by adding 2 to the formula. P= 4n+2 Next, we will make a graph that represents the perimeter of the given figures depending on the number of hexagons.
Using the table, we have three ordered pairs. (1,6) (2,10) (3,14) Plotting these points on the coordinate plane, we can have our graph. Let the x-axis represents the number of the hexagons that a figure has and the y-axis represents the perimeter of the figure.