The word quadrilateral is derived from two Latin words, ‘Quadra’ and ‘latus’. The former word means four, and the latter means sides. So, a quadrilateral is a polygon with four sides. In mathematics, a quadrilateral is a closed, two-dimensional shape with four sides.
In other words, it is a closed shape polygon that consists of four sides, four vertices, resulting in four angles. It is formed by joining at least three non-collinear points.
Definition of a Quadrilateral
Quadrilaterals are polygons with four sides, four vertices, and four angles. While naming a quadrilateral, we should make sure that the name starts and ends in the order of the vertices.
The above polygon ABCD is named based on its four vertices, namely A, B, C, and D. We could also name it as either DCBA, or BCDA, or SDCB, or ABCD. But, it should not be named ACDB or DBCA. It alters the order in which the vertices are formed and hence is not the right way to name a quadrilateral.
The following concepts will help us clear the basic concepts regarding a quadrilateral. After that, we will discuss quadrilaterals in detail, their types and area of a quadrilateral example and so on.
Different Types of Quadrilateral
Now that we havelearnednt what a quadrilateral, is let us understand the different types of quadrilaterals associated with geometry. The different types of quadrilaterals arise due to different angles, sides, and measures.
Although the internal angles of a quadrilateral add up to 360°, the adjacent angles may be the same or different. This characterises the difference in their types.
There are five types of quadrilaterals, and they are listed below.
What are the Properties of a Quadrilateral?
The five types of quadrilateral mentioned above have a different set of properties. Some properties are common to all five, but the majority differs. Some of the common properties of all the types of quadrilaterals are mentioned below.
- Quadrilateral are polygons with four sides.
- Quadrilateral are polygons with two diagonals.
- The sum of all interior angles of a quadrilateral is 360°.
- Quadrilateral are polygons with four vertices.
So, since we now know the common properties, let us closely look at the specific properties of each of these quadrilateral types. We can also identify each of these quadrilaterals with the following properties.
A square is a type of quadrilateral that has four equal sides and therefore four right angles.
Diagonals are perpendicular to each other and bisect each other. The two diagonals are –
BD = AC
So, AC ? BD
This means that the four equal sides are –
BC = CD = AB = DA
Also, there are four right angles. They are –
?C = ?D = ? A= ?B = 90°
There are two pairs of parallel sides. They are –
AD ? BC and AB ? DC
A rectangle is another type of quadrilateral with two pairs of equal and opposite sides parallel to each other and four right angles.
So, a rectangle consists of two pairs of parallel opposite sides. They are –
AD ? BC and AB ? DC
Also, the four right angles are –
?C = ?D = ?A = ?B = 90°
Below are the opposite sides with similar lengths.
AD = BC and AB = DC
The two equal diagonals that bisect each other are given below –
BD = AC
A parallelogram is a type of quadrilateral in which the two pairs of opposite sides are parallel.
A parallelogram has the following properties –
The opposite equal angles in the above parallelogram are –
?Q = ?R and ?P = ?T
The two pairs of parallel sides are given by –
PR ? QT and PQ ? RT
The two diagonals PT and RQ bisect each other.
The opposite sides with the same lengths are –
PR = QT and PQ = RT
A trapezium is another type of quadrilateral in which at least one pair of opposite sides are parallel,. Some of the properties of a trapezium are given below.
Also, the sides of the trapezium that are not parallel are the legs.
In the above-given picture, XW and YZ are the legs of the trapezium
The sides of a trapezium are parallel to each other, which are called bases.
In the above diagram, WZ and XY are the bases of the trapezium.
Moreover, if the two legs or the non-parallel sides are of ual, the trapezium is an isosceles trapezium. The above trapezium is one such example, with the legs XW and YZ being of equal lengths.
A rhombus is a quadrilateral with four equal sides, but the angles formed are not necessarily at right angles.
A rhombus has the following properties –
There are two pairs of parallel sides
AD ? BC and AB ? CD
The four sides of a rhombus are equal in length
BC = AB = AD = DC
The opposite angles of a rhombus are equal.
?B = ?C and ?A = ?D
Diagonals that bisect each other are also perpendicular to each other.
AC ? BD
What is the Area of a Quadrilateral?
The quadrilateral area is the region that is enclosed by all four sides of the quadrilateral. The area is nothing but the region inside the boundary of the figure. Therefore, when we calculate the area of a quadrilateral, we measure them in square units, and the standard unit is meter square. So, since the sides of the different types of quadrilaterals discussed above are not the same, the area differs in each one of them. Now, let us quickly try to understand the area of each type of quadrilateral.
Fastest Way of Finding Area of Quadrilateral
The fastest way of finding the quadrilateral area is by diving the same into two triangles and trying to find their respective areas.
Let us try to find the area of the quadrilateral ABCD given in the above picture.
It is divided into two traingles namely: ABD and CBD.
The diagonal ‘d’ of the quadrilateral ABCD = BD
So, height of ? ABD (h1) = AF;
Also, height of ? CBD (h2) = CE
Therefore, the area of quadrilateral ABCD = Area of ? ABD + Area of ? CBD
= (½ x d x h1) + (½ x d x h2)
= (d x h1) /2 + (d x h2) /2
= d x (h1 + h2) /2
= ½ x d x (h1 + h2)
i.e. Area of a Quadrilateral = ½ x Diagonal x (Sum of heights of the two triangles)
Also, some of the formulas for the different types of quadrilaterals are mentioned below –
|Area||l × b||a²||l × h||½ × d1 × d2||½ × (Sum of parallel sides) × height|
|Perimeter||2 × (l + b)||4a||2 × (l + b)||4a||Sum of all the sides|
There are several real-life applications and usage of quadrilaterals and their area. They are commonly used in the fields of agriculture, landscape design, and architecture. These concepts are widely used in scientific research and the advanced design of maps and navigating systems. They can be easily scaled to near perfection and help determine the research’s scope with precision.