The next shape is made up of 7 squares (four-sided polygon). The 7 squares shape uses 22 matches…

The next shape is made up of 7 squares (four-sided polygon). The 7 squares shape uses 22 matches and has a perimeter of 16. Create a table similar to the one above to help you find a connection between the number of squares, the number of matches and the perimeter of the shape. 7 20 Number of squares Number of matches Perimeter 22 16 TASK 3 [34] Extend your investigation to include regular polygons with 5 (pentagon), 6 (hexagon) and 8 (octagon) sides. For each case: a) draw a shape with at least 7 connecting polygons. (3 x (2) = 6) b) copy and complete a table similar to the one in Task 1. (3 x (7) = 21) c) Complete the summary table below and write down the rule in words you used to find the total number of matches needed for n polygons for ANY polygon. 5 6 8 Number of sides of polygon Number of matches for n polygons [2] TASK 4 Use your findings from tasks 1 to 3 to answer the following: Uses, m and n to write down a general rule which can be used to calculate the number of matches which will be used to create any figure in which several identical polygons have been drawn, with one side attached if: $ = the total number of matches (for 2 attached squares m= 7) m = the total number of sides of the polygon (for a square, s =4) n = the total number of polygons (if we draw 6 squares, n=6)

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