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Jan 23, 2009 · Here's a test to check if a polygon is convex. Consider each set of three points along the polygon--a vertex, the vertex before, the vertex after. If every angle is 180 degrees or less you have a convex polygon. When you figure out each angle, also keep a running total of (180 - angle). For a convex polygon, this will total 360.
- 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?
The properties of the convex polygon are as follows: The interior angle of a convex polygon is strictly less than 180°. A polygon, with at least one interior angle, is greater than 180° is called a non-convex polygon or concave polygon. Sum of all the interior angles of a polygon of n sides = (n – 2)180°. The diagonals of the convex ...
- A convex polygon is a closed shape, where none of the vertices are pointed inward. When a line crosses the convex polygon, it intersects at most th...
- If the interior angles of of the polygon are less than 180 degrees, then the polygon is convex. But if any one of the interior angles is more than...
- A convex polygon can be regular or irregular. It is a closed polygon whose interior angles are less then 180 degrees. No vertices of convex polygon...
- Kite, Pentagon, Hexagon, Heptagon, etc. are examples of convex polygon.
- Based on the shape of polygon, the types of a polygon are convex and concave, regular and irregular, simple and complex.
A convex polygon is a polygon with all interior angles less than 180 ∘ 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. A regular polygon in geometry is always convex. Any closed shape that has a curved surface is convex.
May 30, 2024 · An example of an irregular convex polygon is the scalene triangle. Properties of Convex Polygons. Some of the important properties of convex polygons are: A convex polygon’s diagonals are located within the polygon. A convex polygon is one in which the line connecting every two points is entirely within it.
Aug 3, 2023 · A convex polygon is a polygon that has all its interior angles less than 180°. All the diagonals of a convex polygon lie inside the closed figure. A convex polygon can be both regular and irregular. Regular convex polygons have all sides of the same length and all interior angles of the same measure (less than 180°).
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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 ...
