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polygon closed plane figure bounded by straight line segments as sides. A polygon is convex if any two points inside the polygon can be connected by a line segment that does not intersect any side. If a side is intersected, the polygon is called concave. In a regular polygon the sides are of equal length and meet at equal angles; all other polygons are not regular, although either their sides or their angles may be equal, as in the cases of the rhombus and the rectangle. The simplest regular polygons are the equilateral triangle , the square , the regular pentagon (of 5 sides), and the regular hexagon (of 6 sides). Although the Greeks had developed methods of constructing these four polygons using only a straightedge and compass, they were unable to do the same for the regular heptagon (of 7 sides). In the 19th cent. C. F. Gauss showed that a regular heptagon was impossible to construct in this way. He proved that a regular polygon is constructible with a straightedge and compass only when the number of sides p is a prime number (see number theory ) of the form p  = 2 2n  + 1 or a product of such primes. The first five regular polygons with a prime number of sides that can be constructed using a straightedge and compass have 3, 5, 17, 257, and 65,537 sides.

From Yahoo Answers


Answers:Pentagon Two angles are right angles The other 3 angles add up to 360 degrees

Question:This is a question in my son's 4th grade math assignment! I have read about all of the polygon therories but Im not sure whats right. Thank you in advance -

Answers:Sounds like they are looking for a *right* trapezoid. You can't just say trapezoid, because that doesn't require the shape to have any right angles. A picture of a right trapezoid is given below: (Note: with their clues, it could actually be any polygon with at least 4 sides. For example it could be a five sided polygon, with a couple right angles and one set of parallel sides. (You know, the little house with a pointy roof we all drew when we were little)... and there are other shapes too. But for this question, I'd go with *right* trapezoid.

Question:This is a grade8 challenge from www.aplusclick.com

Answers:The total degrees of the interior angles is (5 - 2)(180) = 540. If there were 5 right angles, the polygon would only have 5*90 = 450 degrees, an absurdity. If there were four right angles, the 5 th angle would have measure 180 degrees, which is impossible in a polygon. Therefore, a 5-sided polygon must have 3 or fewer right angles. To see that a 5-sided polygon can have three right angles, consider an example. First construct a square with a side of length s. Second construct a right triangle with hypotenuse of length s. Align the triangle's hypotenuse with one side of the square. The resulting polygon has five sides and contains exactly three right angles. Therefore, at most three right angles are possible in a polygon with 5 sides. << Answer

Question:4th grade level matimatics book

Answers:Pentagon It has a bottom and then two lines that go up and a point at the top. Kinda like a triangle without a bottom.

From Youtube

Triangles in Polygons :Nicolet film showing that a rightangled triangle can be constructed by making use of the sides of three regular polygons (a pentagon, a hexagon and a decagon). Questions can be set, for example, asking whether these are the only polygons from which a right-angled triangle can be constructed. This might be followed by questions of approximation; eg, When two polygons are chosen, is it possible to find a third which produces a triangle approximating a right-angled triangle? It should be noted that the polygons are inscribed in the same given circle.