# What is a convex polygon?

A

**convex polygon**is a simple**polygon**(not self-intersecting) in which no line segment between two points on the boundary ever goes outside the**polygon**. Equivalently, it is a simple**polygon**whose interior is a**convex**set.A.

### What is the definition of a concave polygon?

A

**concave polygon**is**defined**as a**polygon**with one or more interior angles greater than 180°. It looks sort of like a vertex has been 'pushed in' towards the inside of the**polygon**. Note that a triangle (3-gon) can never be**concave**. A**concave polygon**is the opposite of a convex**polygon**. See Convex**Polygon**.#### Is every equilateral polygon convex?

Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a**regular polygon**. If the number of sides is at least five, an**equilateral polygon**need not be a**convex polygon**: it could be concave or even self-intersecting.#### Is a triangle a convex or concave polygon?

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 by Convex?

curving or bulging outwards. physics having one or two surfaces curved or ground in the shape of a section of the exterior of a sphere, paraboloid, ellipsoid, etca**convex**lens. maths (of a polygon) containing no interior angle greater than 180°

B.

### What is a convex or concave shape?

**Concave**is an adjective that describes a surface that curves inward, or is thinner in the middle than on the edges. In ordinary usage,

**concave**and

**convex**are typically used when referring to glass surfaces, like the lenses of optical viewing equipment. The side mirror of a car has a

**concave**surface.

#### Is Water concave or convex?

A**concave**meniscus, which is what you normally will see, occurs when the molecules of the liquid are attracted to those of the container. This occurs with**water**and a glass tube. A**convex**meniscus occurs when the molecules have a stronger attraction to each other than to the container, as with mercury and glass.#### Are glasses convex or concave lenses?

Nearsighted people (people who see close objects fine but distant objects appear blurry) have concave**lenses**in their glasses to correct their vision. A convex**lens**is thinner at the edges and thicker towards the center. Convex**lenses**are bent towards a central point.#### What is a convex graph?

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.

C.

### Can a shape be convex and 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**. Take note of what it takes to make the polygon either**convex**or**concave**. Also change the number of sides.#### What is a concave shape?

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.#### Are all convex polygons regular?

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.#### What is the sum of the interior angles of a convex polygon?

**Theorem**39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. The polygon in Figure 1 has seven sides, so using**Theorem**39 gives: An exterior angle of a polygon is formed by extending only one of its sides.

Updated: 3rd December 2019