Suppose we have to cover the xy-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can…

Question

Suppose we have to cover the xy-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes; equilateral triangle, square, regular pentagon, regular hexagon. Then the tiling can be done with tiles of -

MARKS Content Team · Accepted Answer

Correct answer: (B) exactly three of the four shapes. We can cover the plane using squares definitely using equilateral triangle, we can also cover the plane. Also regular hexagon is made of equilateral triangles. But pentagon cannot cover the plane because of its shape.

Suppose we have to cover the xy-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes; equilateral triangle, square, regular pentagon, regular hexagon. Then the tiling can be done with tiles of -

Solution

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