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Type: Open-Ended
Category: Two Dimensional Shapes
Level: Grade 10
Standards: HSG-MG.A.3
Author: nsharp1
Created: 4 years ago

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Two Dimensional Shapes Question

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Tessellation, or tiling, refers to covering a surface with shapes so that there are no gaps or overlaps. These can be different shapes, or the same shape. In the questions that follow, a regular tessellation will be considered- that is, a tessellation that uses only one type of regular polygon.

Grade 10 Two Dimensional Shapes CCSS: HSG-MG.A.3

Jonathan is retiling his large, rectangular kitchen with a surface area of about 700 square feet. He can choose tiles shaped like any regular polygon, but can only choose one shape. He will use partial tiles along the edges, if necessary (partial tiles being tiles that he has cut). Also, regardless of the shape he chooses, all the individual tiles will have the same surface area (roughly 0.75 square feet). If he wants to minimize the amount of grout he will need (the substance that is placed between the tiles, which are spaced about a quarter inch away from each other), which shape of tile should he use? Explain.