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The intuitive, but wrong, answer is that it must be regular. It need not be.
For example, a hexagon with 6 angles, each measuring 120 degrees is not necessarily regular but it will tessellate. In fact, the angles could be
(30, 120, 120, 120, 30, 300) degrees - a chevron, like an armed forces stripe, or
(30, 30, 300, 30, 30, 300) degrees - a Z shape, or
(90, 90, 90, 90, 90, 270) degrees. an L shape.
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∙ 8y ago
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Which polygons do not tessellate?
Pentagons, decagons, and octagons will not tessellate. In order to create a tessellation, the sum of the angles at a point must be 360.
True or false p lies in plane b the line containing p and q must lie in plane b?
False. In order for the line PQ to lie in plane B, then both P and Q must lie in plane B.
Does a regular octagon tessellate?
No, because if you use the formula to find an angle measure: 180(n-2)/n (this formula only works for regular shapes) where n is the number of sides, then the measure of one of the angles equals 135. Then in order to tessellate 135 must be a multiple of 360. But 135 x 2 = 270, and 135 x 3 = 405, so a regular octagon does not tessellate.
Why must a regular polygon's interior angles have a measure that is a divisor a 360?
The statement is not correct. The sum of the interior angles of an n-sided polygon is (n-2)*180 degrees. If n is odd, the sum will not be a divisor of 360. And each individual interior angle will be 180*(n-2)/n degrees. And that will be a divisor of 360 only if n = 3 (triangle), 4 (square) or 6 (hexagon). And, not by coincidence, these are the only regular polygons that will tessellate a plane surface.
What is the relationship between a tessellation and an angle?
The interior angle of a regular polygon must be a factor of 360 degrees for it to tessellate uniformly.
What must be the sum of all interior angles that meet at a vertex if a figure is to tessellate a plane?
360 degrees
Which polygons do not tessellate?
Pentagons, decagons, and octagons will not tessellate. In order to create a tessellation, the sum of the angles at a point must be 360.
Why does a regular pentagon wont tessellate and a regular hexagon will?
The interior angle of a regular pentagon is 108 degrees, whereas that of a hexagon is 120 degrees.At the point where the tessellating polygons meet, the sum of all the angles must be 360 degrees. 108 does not divide 360 evenly whereas 120 does.
Why does a regular pentagon not tessellate the plane?
In order for a polygon to tessellate, the angles must add up to 360 degrees, to come full circle. Triangles have 60 degree angles, so 6 of them circle together. Squares have 90 degree angles, so 4 of them tessellate to a point. Hexagons can even tessellate, because the 120 degree angles add up to 360. But pentagons have 108 degree angles. Three of them add up to 324, only leaving 36 degrees left to close the circle.
What must the sum of the be for it to tessellate?
360 degrees.
How long must each side of a hexagon be to measure 25 inches across the widest part?
Each side of a hexagon must be 12.5 inches in order for the widest part to be 25 inches across.
Explain why a regular nonagon does not tessellate?
because there are to many sides * * * * * Each interior angle of a regular nonagon is 140 degrees. At any point in the tessellated plane, a whole number of shapes must come together and the sum of their interior angles must be 360 degrees. 140 does not go into 360 and so a regular nonagon cannot tessellate.
Why can't circles tessellate?
For a shape to tile a plane, it must be capable of sharing a border with a copy of itself. Circles cannot do this; two circles which do not overlap touch in at most one point.
Does hexagon have obtuse angle?
Yes. A hexagon must have an obtuse angle.
Formula for area of a hexagon?
The question does not state that it is a regular hexagon and so you may not assume that it is. Therefore, there is no simple formula because a hexagon can have very many shapes. One method would be to pick a point in the plane of the hexagon and join it to all the vertices. This divides up the hexagon into triangles. Their areas can be calculated using base and height, or three sides, or two sides and included angle - whichever you like. Finally the areas of the triangles must be combined to get the area of the hexagon.
True or false p lies in plane b the line containing p and q must lie in plane b?
False. In order for the line PQ to lie in plane B, then both P and Q must lie in plane B.
Can a tesellation be created with any shape you can think of?
No. Multiple copies of the shape - whether arranged side-by-side or in an interlocking pattern, must cover a plane area without gaps or overlaps. A circle or regular pentagon, for example, will not tessellate.
