## What is a four sided figure and convex?

A convex quadrilateral is a four sided polygon that has interior angles that measure less than 180 degrees each. The diagonals are contained entirely inside of these quadrilaterals. Convex quadrilaterals can be classified into several sub-categories based on their sides and angles.

### What is a 4 sided shape?

Definition: A quadrilateral is a polygon with 4 sides.

#### What is convex quadrilateral explain with a figure?

Hint: A convex quadrilateral is a quadrilateral which has all interior angles less than 180 degrees and all the diagonals lie within the quadrilateral. In the case of a rectangle, we see (in the below figure) that all the interior angles are 90 degrees (thus less than 180 degrees).

What is a convex figure?

A convex polygon is a closed figure where all its interior angles are less than 180° and the vertices are pointing outwards. The term convex is used to refer to a shape that has a curve or a protruding surface. In other words, all the lines across the outline are straight and they point outwards.

What is a 4 sided irregular shape called?

A quadrilateral is a four-sided and four-angled shape. A regular quadiralteral is a quadrilateral with all of its sides having the same length. An irregular quadrilateral is a quadrilateral that is not regular, so all of its sides do not have equal length.

## What is a 4 sided shape with unequal sides?

Quadrilaterals are polygons with four sides (hence the beginning “quad”, which means “four”). A polygon with non-equal sides is called irregular, so the figure that you are describing is an irregular quadrilateral. This figure has side lengths of 1, 2, 3, and 4 respectively, so it is an irregular quadrilateral.

### What is a 4 sided shape but not a square?

A rhombus is a four-sided shape where all sides have equal length (marked “s”). Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines) meet in the middle at a right angle.

#### What is the difference between concave and convex quadrilateral?

Concave quadrilaterals are those that have a cavity, or a cave. A convex quadrilateral has both diagonals completely contained within the figure, while a concave one has at least one diagonal that lies partly or entirely outside of the figure.

A kite is a convex quadrilateral as the line segment join any two opposite vertices inside it, lies completely inside it.

What is a convex side?

Curved outwards. Example: A polygon (which has straight sides) is convex when there are NO “dents” or indentations in it (no internal angle is greater than 180°) The opposite idea is called “concave”. See: Concave. Polygons.

## What are concave and convex figures?

Concave describes shapes that curve inward, like an hourglass. Convex describes shapes that curve outward, like a football (or a rugby ball).

### What shape has 4 sides 4 angles?

A quadrilateral is a polygon that has exactly four sides. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)

#### Which is the best description of a convex function?

Here are some of the topics that we will touch upon: \Convex, concave, strictly convex, and strongly convex functions \First and second order characterizations of convex functions \Optimality conditions for convex problems 1 Theory of convex functions 1.1 De\\fnition

How can you tell if a quadrilateral is concave or convex?

Another means of determining if a quadrilateral is concave is to check the diagonals, or the line segment that connects non-adjacent vertices. If any part of a diagonal is on the exterior of the quadrilateral, then the quadrilateral is concave. If a shape is concave, then it will appear to have a side that has been pushed in or have a cave.

Which is the second order characterization of a convex function?

Second order su\cient condition: r2f(x) ˜0; 8×2 )fstrictly convex on : The converse is not true though (why?). First order characterization: A function fis strictly convex on \nif and only if f(y) >f(x) + rfT(x)(y x);8x;y2 ;x6=y: 8 There are similar characterizations for strongly convex functions.

## When is a convex function f Rn Ris convex?

A function f: Rn!Ris convex if and only if the function g: R!Rgiven by g(t) = f(x+ ty) is convex (as a univariate function) for all xin domain of f and all y2Rn. (The domain of ghere is all tfor which x+ tyis in the domain of f.)