Does a regular decagon tessellate?
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shapes that don't overlap and there are no spaces or gaps between the shapes. These are also sometimes called tilings of a plane. When a single shape can be used to create a tessellation of a plane, we say that it tessellates, and there are special rules for determining if certain shapes tessellate or not.
Answer and Explanation:
A regular decagon does not tessellate.
A regular polygon is a two-dimensional shape with straight sides that all have equal length. A regular decagon is a 10-sided regular polygon. As it turns out, there are only three regular polygons that can be used to tessellate the plane: regular triangles, regular quadrilaterals, and regular hexagons. The reason for this lies in the measurements of the interior angles of a regular polygon.
For a regular polygon to tessellate the plane, each interior angle must be a divisor of 360° because then there won't be any gaps where the polygons meet at each vertex. This is why a regular triangle, quadrilateral, and hexagon can be used to tessellate the plane.
The interior angles of a regular triangle are each 60°, and 360° ÷ 60° = 6.The interior angles of a regular quadrilateral are each 90°, and 360° ÷ 90° = 4.The interior angles of a regular hexagon are each 120°, and 360° ÷ 120° - 3.
Now consider a regular decagon. The interior angles of a regular decagon each have measure 144°, and 360° ÷ 144° = 2.5, so 144° is not a divisor of 360°. Therefore, a regular decagon cannot be used to tessellate the plane.
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Answer and Explanation:
A regular decagon does not tessellate.
A regular polygon is a two-dimensional shape with straight sides that all have equal length. A regular decagon is a 10-sided regular polygon. As it turns out, there are only three regular polygons that can be used to tessellate the plane: regular triangles, regular quadrilaterals, and regular hexagons. The reason for this lies in the measurements of the interior angles of a regular polygon.
For a regular polygon to tessellate the plane, each interior angle must be a divisor of 360° because then there won't be any gaps where the polygons meet at each vertex. This is why a regular triangle, quadrilateral, and hexagon can be used to tessellate the plane.
The interior angles of a regular triangle are each 60°, and 360° ÷ 60° = 6.The interior angles of a regular quadrilateral are each 90°, and 360° ÷ 90° = 4.The interior angles of a regular hexagon are each 120°, and 360° ÷ 120° - 3.
Now consider a regular decagon. The interior angles of a regular decagon each have measure 144°, and 360° ÷ 144° = 2.5, so 144° is not a divisor of 360°. Therefore, a regular decagon cannot be used to tessellate the plane.
Learn more about this topic:
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