What is a Quadrilateral?

A regular polygon having four vertices, angles, and sides respectively which is geometrically closed can be defined as the quadrilateral. The term quadrilateral has been derived or excavated from the Latin words/terms, ‘quadra’ which basically signifies the number four, and ‘latus’ which means sides. In total, a quadrilateral means a shape of four sides. There are various types of quadrilaterals such as a trapezium, a square, a parallelogram, a rhombus, a kite, a rectangle. On the basis of the length of their sides, they are briefly categorized. In this article, we will try to understand various topics related to it such as properties of quadrilaterals, characteristics of its types, and do a detailed analysis about them. 

Area of Quadrilateral 

The space or region which is enclosed/covered by the four sides of a quadrilateral can be defined as the area of a quadrilateral. We know that area is a region that is occupied inside the figure or an object. Mathematically the area of the quadrilateral is given by, ½ * by diagonal * addition of the height of triangles (two). 

The formula mentioned above is generally used for some calculations, but there are other formulas for it as well such as heron’s formula. In the next few paragraphs, we will deal with the examples related to its area in order to grasp the concept in a detailed manner. 

Some Calculations Based on The Area of Quadrilateral 

In this section, we will try to cover the examples of the area of a quadrilateral using the general formula for it. Some of the examples are mentioned below.

Example 1:

Find the area of a quadrilateral if the diagonal measures about 10 cm and the heights of the two triangles are 2 cm and 6 cm respectively?

Given that,

Diagonal measures = 10 cm 

Height 1 = 2 cm 

Height 2 = 6 cm 

Using the general formula for Area of quadrilateral,  ½ * by diagonal * addition of the height of triangles,

½ * 10 * ( 6 + 2 )

½ * 10 * 8 = 40 cm square units. 

Example 2:

Find the area of a quadrilateral if the diagonal measures about 12 cm and the heights of the two triangles are 3 cm and 8 cm respectively?

Given that,

Diagonal measures = 12 cm 

Height 1 = 3 cm 

Height 2 = 8 cm 

Using the general formula for Area of quadrilateral = ½ * by diagonal * addition of the height of triangles,

½ * 12 * ( 3 + 8 )

½ * 12 * 11 = 66 cm square units. 

Some Important Properties of a Quadrilateral 

The following points mentioned below analyses the properties of a quadrilateral.

  1. Each type of quadrilateral has four vertices, angles, and sides respectively. The four sides of the quadrilateral are AB, CD, BC, and DA.
  2. The sum of the interior angles of a quadrilateral result in the value of 360 degrees, specifying that every angle measures about 90 degrees.
  3. A quadrilateral is divided into 6 types such as trapezium, rhombus, rectangle, square, kite, and a parallelogram.
  4. On the basis of the lengths of the sides, they are classified into such types.

Properties of Its Types 

The following points mentioned below signify the properties of the quadrilateral in a brief way.

  1. Square: Every side is equal and parallel to each other where diagonals bisect each other.
  2. Rectangle: Opposite sides are equal and parallel to each other where diagonal bisect them.
  3. Rhombus: All four sides are equal in length, opposite sides and angles are parallel and equal to each other respectively.
  4. Parallelogram: The opposite sides, angles are of the same length, equal to each other and parallel respectively. 
  5. Trapezium: Only one pair of sides which are opposite is parallel to each other.
  6. Kite: Only one pair of the angles which are opposite is of the same length.

If you want to learn about quadrilaterals in a detailed manner, in a fun way, and in an interactive manner, you may visit the Cuemath website.

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