In this chapter we will learn about the concept of convex and concave quadrilateral with solved examples.

## What is Convex Quadrilateral ?

The quadrilateral in which all interior angle is less than 180 degree is called convex quadrilateral.

Given below are features of convex quadrilateral:

(a) all four angle measures less than 180 degree

(b) the diagonals lie inside the polygon

(c) all set of sides point outwards

For Example;

Given above is the convex polygon ABCD in which;

(a) All angles are less than 180 degree.

Here;
∠A = 127 degree
∠B = 82 degree
∠C = 87 degree
∠D = 63 degree

(b) Note that all set of sides are pointing outwards.

In the above image, note the sides DA and BA are pointing in outward direction.

(c) Both the diagonals AC and BD lie inside the quadrilateral shape.

A quadrilateral in which one or more interior angle is greater than 180 degree is called Concave Quadrilateral.

(a) One of the angle is greater than 180 degree

(b) one or more diagonal extend outside the body of quadrilateral

(c) One or more pair of side are in inward direction.

For Example;

Given above is the concave quadrilateral in which;

(a) Angle D is greater than 180 degree

(b) Side AD and CD are inwards direction

(c) One of the diagonal AC extends in outward direction.

## FAQ’s on convex and concave quadrilateral

(01) Is rectangle a concave quadrilateral?

No !!
In rectangle all angles measure 90 degree. Hence it is a convex quadrilateral.

(02) What type of quadrilateral is the Rhombus ?

Rhombus is a convex quadrilateral since its all the interior angles are less than 180 degree.

(03) Any real life example of concave quadrilateral ?

The below electric guitar is an example of concave quadrilateral.