Polygon From Wikipedia‚ the free encyclopedia Jump to: navigation‚ search For other uses‚ see Polygon (disambiguation). Some polygons of different kinds In geometry a polygon ( /ˈpɒlɪɡɒn/) is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. A polygon is traditionally a plane figure that is bounded by a closed path‚ composed of a finite sequence of straight line segments (i.e.‚ by a closed polygonal chain). These segments are called its edges or sides
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Polygon names | Name | Edges | Remarks | henagon (or monogon) | 1 | In the Euclidean plane‚ degenerates to a closed curve with a single vertex point on it. | digon | 2 | In the Euclidean plane‚ degenerates to a closed curve with two vertex points on it. | triangle (or trigon) | 3 | The simplest polygon which can exist in the Euclidean plane. | quadrilateral (or quadrangle or tetragon) | 4 | The simplest polygon which can cross itself. | pentagon | 5 | The simplest polygon which can exist
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Name LESSON Date Class Reteach Developing Formulas for Circles and Regular Polygons Circumference and Area of Circles 9-2 A circle with diameter d and radius r has circumference C d or C 2 r. A circle with radius r has area A 2 r . Find the circumference of circle S in which A Step 1 Use the given area to solve for r. A 81 cm 2 2 81 cm . r2 r r2 r 2 Area of a circle Substitute 81 for A. Divide both sides by . Take the square root of both sides. cm 81 cm2 9 cm
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sides meet at every vertex. Types of Polygons Regular - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral. Equiangular - all angles are equal. Equilateral - all sides are the same length. | Convex - a straight line drawn through a convex polygoncrosses at most two sides. Every interior angle is less than 180°. | | Concave - you can draw at least one straight line through a concave polygon that crosses more than two sides. At least
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Polygons in our life The importance of polygons would probably relate to the variety of polygon shape often used in the building of modern structures. The triangle‚ for instance‚ is often used in construction because its shape makes it comparatively strong. The use of the polygon shape reduces the quantity of materials needed to make a structure‚ so essentially reduces costs and maximizes profits in a business environment. Another polygon is the rectangle. The rectangle is used in a number of
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Polygon/Circle |P = Perimeter C = Circumference distance around the polygon/circle | A = Area the surface inside the boundary( perimeter) | | |triangle | [pic] |[pic] | |a = altitude |P = b + c + d |A = 1/2ab | |b = base |or |Note:
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E Properties of Plane Areas Notation: A area x‚ y distances to centroid C Ix‚ Iy moments of inertia with respect to the x and y axes‚ respectively Ixy product of inertia with respect to the x and y axes IP Ix Iy polar moment of inertia with respect to the origin of the x and y axes IBB moment of inertia with respect to axis B-B 1 y x h C b y x Rectangle (Origin of axes at centroid) A Ix bh bh3 12 x Iy b 2 hb3 12 y h 2 Ixy 0 IP bh 2 (h 12 b2) 2 y B Rectangle (Origin of axes
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Find the sides of each of the two polygons if the total number of sides of the polygons is 13‚ and the sum of the number of diagonals of the polygons is 25. Assume: 8 and 5 D1= n2(n-3) n=13 D1= 82(8-3) D=25 D1= 20 D2= n2(n-3) D2= 52(5-3) D2= 5 Answer: The number of sides in each polygon is 8 and 5 #17. What is the name of a regular polygon that has 90 diagonals? Given: D = 90 Required: Name of regular polygon D = n2 (n-3)
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tessellations. Math Behind Tessellations In order to create a regular tessellation the first step is to choose one single regular polygon‚ whether it be an equilateral triangle‚ a square‚ or a hexagon‚ these three regular polygons are the only prototiles that will tile the field with no overlaps or gaps when completed. The rule for regular polygon is that all sides are the same length and all angles are of the same degree. A regular polygon has rotational and reflexive symmetry. Reflectional symmetry
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assemble a heptagon? (A) Two (B) Three (C) Five (D) Triangles cannot be combined to form a heptagon If the interior angles of a polygon sum to 720 degrees‚ how many vertices does that polygon have? (A) Four (B) Five (C) Six (D) The sum of the interior angles of a polygon never equals 720 degrees A rectangle is an example of what? (A) An equilateral polygon (B) A parallelogram (C) A closed curve (D) Answers (b) and (c) Given that the quadrilateral pictured is a parallelogram‚ what is
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