What Is Concave Quadrilateral?

Are you curious to know what is concave quadrilateral? You have come to the right place as I am going to tell you everything about concave quadrilateral in a very simple explanation. Without further discussion let’s begin to know what is concave quadrilateral?

Quadrilaterals, the geometric shapes with four sides, can take various forms, each possessing unique properties. Among them is the concave quadrilateral, a fascinating figure that showcases intriguing curves and angles. In this blog post, we will delve into the concept of a concave quadrilateral, its characteristics, and the mathematical principles that define its structure. Join us as we embark on a geometric exploration and unravel the secrets behind this captivating shape.

What Is Concave Quadrilateral?

A concave quadrilateral is a polygon with four sides where at least one of its interior angles is greater than 180 degrees. This property creates inward curves or indentations within the shape, making it visually distinct from its convex counterpart. These curves give the concave quadrilateral a unique aesthetic appeal and contribute to its mathematical properties.

Characteristics Of Concave Quadrilaterals:

  1. Interior Angles: The defining characteristic of a concave quadrilateral is the presence of an interior angle greater than 180 degrees. The other three interior angles will be less than 180 degrees, as in any quadrilateral.
  2. Vertex Arrangement: The vertices of a concave quadrilateral are not arranged in a way that creates a convex shape. Instead, they are positioned in such a manner that the interior angles extend beyond 180 degrees, forming the concave features.
  3. Diagonals: Diagonals are line segments connecting non-adjacent vertices of a polygon. In concave quadrilaterals, at least one diagonal lies outside the shape or intersects with the extension of one of the sides.

Examples Of Concave Quadrilaterals:

  1. Bowtie Shape: A common example of a concave quadrilateral is a bowtie shape. It consists of two pairs of opposite congruent sides that intersect each other, creating inward curves.
  2. Hourglass Shape: Another example of a concave quadrilateral is the hourglass shape. It features a narrow waistline and two bulging sections above and below the waist, forming concave curves.
  3. Star Shape: Certain star-shaped figures can also be considered concave quadrilaterals. These shapes have multiple intersecting sides and inward curves, resulting in interior angles greater than 180 degrees.

Mathematical Considerations:

  1. Area Calculation: The calculation of the area of a concave quadrilateral requires subdividing it into smaller polygons or triangles. Each subdivided section’s area can be calculated separately, and the sum of these areas yields the total area of the concave quadrilateral.
  2. Convex Decomposition: Convex decomposition is a process of dividing a concave quadrilateral into multiple convex polygons, making it easier to analyze and work with mathematically. This technique simplifies calculations and enables the application of formulas specific to convex polygons.


The concave quadrilateral is an intriguing geometric shape that showcases inward curves and angles greater than 180 degrees. It distinguishes itself from its convex counterparts, capturing our attention with its unique aesthetics and mathematical properties. Exploring the characteristics and properties of concave quadrilaterals allows us to appreciate the beauty and complexity of geometric shapes. So, let us continue our journey through the fascinating world of polygons and uncover the secrets hidden within their curves and angles.


What Is A Concave Quadrilateral?

A quadrilateral which has one of its interior angles greater than 180°, is known as a concave quadrilateral.

What Is A Convex And Concave Quadrilateral?

(i) A convex quadrilateral is a quadrilateral whose diagonals lie in the interior of the Quadrilateral. If any of the diagonals is not in the interior of the Quadrilateral, it is called a Concave Quadrilateral. (ii) The sum of all the angles of a Quadrilateral =360∘

What Do You Mean By Convex Quadrilateral?

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 Called Concave?

: hollowed or rounded inward like the inside of a bowl. a concave lens. : arched in : curving in. used of the side of a curve or surface on which neighboring normals to the curve or surface converge and on which lies the chord joining two neighboring points of the curve or surface. concave.


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