In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star.
Herein, is a regular polygon convex or concave?
A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a ‘bulging’ polygon. Note that a triangle (3-gon) is always convex.
What does it mean if a polygon is concave?
A concave polygon is a polygon that is not convex. A simple polygon is concave iff at least one of its internal angles is greater than . An example of a non-simple (self-intersecting) polygon is a star polygon. A concave polygon must have at least four sides.
Can a Pentagon be concave?
Concave or Convex. A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
What is not a regular polygon?
The simplest polygon is a triangle (a 3-sided shape). Polygons of all types can be regular or irregular. A regular polygon has sides of equal length, and all its interior angles are of equal size. Irregular polygons can have sides of any length and angles of any size. In fact, they are the only polygons which do.
What is concave and convex polygon?
A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive.
Which polygon has an interior angle sum of 1080?
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees.
Is a circle a regular polygon?
Polygons. A polygon is a closed plane figure with three or more sides that are all straight. The following figure is not a polygon as it is not a closed figure. A circle is not a polygon as it does not have straight sides.
What is a convex shape?
Equivalently, it is a simple polygon whose interior is a convex set. In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees.
Is a right triangle a regular polygon?
In an equilateral polygon, each side has the same length. In triangle ABC below, all sides are 12 feet making triangle ABC equilateral. A regular polygon is BOTH equiangular and equilateral. A square is a regular polygon because all sides have the same length and all angles measure the same: 90 degrees.
Is a circle a convex?
The interiors of circles and of all regular polygons are convex, but a circle itself is not because every segment joining two points on the circle contains points that are not on the circle. A set in a space that is not convex is called a concave set.
What is true about a regular polygon?
For a polygon to be ‘regular’ it must have all sides the same length and all interior angles the same. The figure on the right is actually an example of an equilateral polygon since it has all sides the same length, but it is not a regular polygon because its interior angles are not all the same.
Is a star a polygon?
In geometry, a star polygon is a type of non-convex polygon. Only the regular star polygons have been studied in any depth; star polygons in general appear not to have been formally defined. The first usage is included in polygrams which includes polygons like the pentagram but also compound figures like the hexagram.
How many sides does an N Gon?
A polygon has as many angles as it has sides. For example, a triangle has 3 sides and 3 angles. A pentagon has 5 sides and 5 angles. An octadecagon has 18 sides and 18 angles!
What is a simple polygon?
In geometry a simple polygon /ˈp?l?g?n/ is a flat shape consisting of straight, non-intersecting line segments or “sides” that are joined pair-wise to form a closed path. A polygon encloses a region (called its interior) which always has a measurable area.
Is a polygon a square?
Polygons are many-sided figures, with sides that are line segments. Polygons are named according to the number of sides and angles they have. The most familiar polygons are the triangle, the rectangle, and the square. A regular polygon is one that has equal sides.
Is a regular polygon a parallelogram?
A parallelogram has opposite sides that are parallel. Squares, rectangles and rhombi are parallelograms with four right angles. A trapezoid has one pair of parallel sides. A regular polygon has congruent sides and angles.
What is convex line?
In mathematics, a real-valued function defined on an n-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.
What makes a regular polygon?
A polygon is regular when all angles are equal and all sides are equal (otherwise it is “irregular”). This is a regular pentagon (a 5-sided polygon). See: Polygon. Regular Pentagon. Area = 21.398771616641.
Is a triangle is a polygon?
Polygons – Triangles – First Glance. As you learned in the last lesson, a triangle is the simplest polygon, having three sides and three angles. The sum of the three angles of a triangle is equal to 180 degrees. Triangles are classified by sides and by angles.
Is a rectangle a regular polygon?
A regular polygon must be both equilateral (all sides are the same length) and equiangular (all angles of the same measure). A rectangle is equiangular. All of its sides equal 90˚ by definition. All of its sides can never be the same length and so, it can never be regular.
What is the sum of a polygon?
The formula for calculating the sum of the interior angles of a regular polygon is: (n – 2) × 180° where n is the number of sides of the polygon. This formula comes from dividing the polygon up into triangles using full diagonals. We already know that the interior angles of a triangle add up to 180°.
Is an octagon a convex or a concave?
Concave or Convex. A convex octagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
How many sides are there in a convex polygon?
The sum of the exterior angles of any convex polygon is 360 degrees. That means that if you have n sides, then each exterior angle of a regular polygon is 360/n. If you can find out how the exterior angle is related to the interior angle, you can finish the solution.