ACE problems Extension 17.

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Presentation transcript:

ACE problems Extension 17

Problem Suppose you tie together the ends of a piece of string to form a loop that is 30 units long. A unit is equal to the length of a side of one floor tile.

Wave 1 Suppose you arranged the string to form an equilateral triangle. What would the area of the enclosed space be? What would the area be if you formed a square? What would the area be if you formed a regular hexagon?

Wave 2 Of all the rectangles with a perimeter of 30 units, which has greatest area?

Wave 3 Of all the triangles with a perimeter of 30 units, which has greatest area?

Wave 4 How does the area of a regular octagon with a perimeter of 30 units compare to the areas of a triangle, square, and a hexagon with perimeters of 30 units?

Wave 5 What happens to the enclosed area as the 30-unit perimeter is used to make regular polygons of more and more sides?

Wave 6 As the number of sides of a polygon gets larger and larger, what shape does the polygon eventually resemble?