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In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). [1] Equivalently, a polygon is convex if every line that ...
- Regular Convex Polygon
- Irregular Convex Polygon
- Area of A Convex Polygon
- Sum of Interior Angles
- Sum of Exterior Angles
- Topics Related to Convex Polygon
A regular convex polygon is a polygon where each side is of equal length, and all the interior angles are equivalent and less than 180°. The vertices of the polygon are equidistant from the center of the regular polygon. For example, a regular convex pentagon is an example of a regular convex polygon.
An irregular convex polygon is a polygon where each side is of unequal length, and all the interior angles are of unequal measure. Example: irregular parallelogramis an example of an irregular convex polygon. Convex and concave shapes are different. The table below shows the differences between convex and concave polygon. A polygon is a shape that ...
The space covered inside the boundary of a convex polygon is its area. Considering the coordinates of a convex polygon to be (x1x1, y1y1), (x2x2, y2y2), (x3x3, y3y3), .....(xnxn, ynyn), its area is given by, Area = 1/2 |(x1x1y2y2 - x2x2y1y1) + (x2x2y3y3 - x3x3y2y2) + + (xnxny1y1 - x1x1ynyn)|
The sum of interior angles of a convex polygon with 'n' sides is given by the formula, 180(n-2)°. For example, a hexagon has 6 sides. So the sum of its interior angles is 180(6-2)°, which is equal to 720°.
The sum of exterior angles of a convex polygon is equal to 360°/n, where 'n' is the number of sides of the polygon.
Check out some interesting articles related to Convex Polygon: 1. Definition of Polygon 2. Polygon Shape 3. Similarity in Triangles 4. Areas of Similar Triangles 5. What is Similarity?
Apr 16, 2016 · If the 2D analog of the vector cross product between consecutive pairs of edge vectors in a polygon has differing signs (ignoring zeroes, as if they had no sign), the polygon must be concave.
Jan 23, 2009 · The polygon is convex if the z-components of the cross products are either all positive or all negative. Otherwise the polygon is nonconvex. If there are N points, make sure you calculate N cross products, e.g. be sure to use the triplets (p [N-2],p [N-1],p [0]) and (p [N-1],p [0],p [1]).
5 days ago · A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an indented pentagon is not (right figure).
Regularly, a polygon is firmly convex, if each line segment with two nonadjacent vertices of the polygon is strictly internal to the polygon but on its endpoints. Each non-fragment triangle is definitely convex.
A convex polygon is a polygon with all interior angles less than $180^\circ$ and vertices are pointed outwards. In convex polygons, all diagonals are in the interior of the polygon. All the vertices of a complex polygon point outwards.
