 In Euclidean plane geometry, a mathematical system described in the textbook on geometry provided by Alexandrian Greek mathematician -Euclid, a quadrilateral is defined as a polygon with four sides or edges and four vertices or corners.

Derived from the two Latin words - quadri meaning "a variant of four" and latus that means "side,". Quadrilaterals can be simple (not self-intersecting), complex (self-intersecting), convex or concave. The sum of all interior angles of a simple quadrilateral, let's say ABCD, calculates 360 degrees of arc.

For instance, ∠A + ∠B + ∠C + ∠D = 360°.

In mathematics, there are several quadrilaterals as per Euclidean plane geometry. However, some of the common ones include Square, Rectangle, and Trapezium.

After going through the above-given information, you hopefully have become a bit familiar with the concept of quadrilaterals in mathematics. Nevertheless, to get a clear insight into the same, let's have a look at some types of quadrilaterals.

1. Trapezium

Trapezium in English or trapezoid in Canadian or American English is a convex quadrilateral having at least one pair of opposite sides parallel. If we consider looks, then a trapezium appears as a triangle with its top sliced off parallel to its bottom. In general, this mathematical shape seems sitting with its longest side down, in addition to two sloping sides as edges connecting parallel sides.

Characterizations:

Area: ½ x Sum of the lengths of the parallel sides x Perpendicular distance between parallel sides.

Perimeter: Sum of lengths of all sides.

Number of Vertices: Four (4).

Line of Symmetry: Zero (0).

Number of Edges: Four (4).

Properties: One pair of opposite sides are parallel, the Sum of adjacent angles is 180°, and convex polygon.

Real-life Examples

A few out of many examples of a trapezium are the face of a popcorn box, bridges, and handbags.

1. Parallelogram

The parallelogram is a simple quadrilateral with two pairs of opposite sides parallel. The opposite sides of a parallelogram are not just parallel but also of equal length, and therefore, its opposite angles are of equal measure. In particular, a parallelogram is a mathematical shape with four sides, out of which the opposite ones are parallel and equal in length. Its opposite angles are equal, and consecutive angles are supplementary, i.e., the sum of its consecutive angles is equal to 180°.

Characterizations:

Area: Base × Height

Perimeter: 2 x Sum of lengths of adjacent sides

Number of Vertices: Four (4)

Number of Edges: Four (4)

Line of Symmetry: Zero (0)

Properties: Opposite sides are parallel and congruent, opposite angles are equal and congruent, diagonals bisect each other, and convex polygon.

Real-life Examples

Examples of parallelograms include tables, desks, and the Dockland office building in Hamburg, Germany.

1. Rectangle

A rectangle is a quadrilateral with four sides, four corners, and four right angles. The opposite sides of a rectangle are of the same length and parallel. Besides, each of its four angles measures 90°. Due to these aspects, it can also be defined as a parallelogram where all interior angles are right angles.

Characterizations

Area: Length × Width

Perimeter: 2 x (Length + Width)

Number of Vertices: Four (4)

Number of Edges: Four (4)

Internal Angles: All 90°

Properties: Convex polygon, isogonal figure, and diagonals are congruent and bisect each other.

Real-life Examples

Some of several examples of rectangle encompass license plates, dollar bills, a page in a book, and cards (like in a deck of cards).

1. Square

In mathematics or we can say geometry, a square is a regular quadrilateral with four equal sides and four equal angles measuring 90° each. A square can also be defined as a four-sided flat shape that appears as a rectangle in which two adjacent sides are of equal length.

Characterizations

Area: Side x side or (side)2

Perimeter: 4 X Side

Number of Vertices: Four (4)

Number of Edges: Four (4)

Internal Angles: All 90°

Type: Regular quadrilateral or regular polygon

Properties: Convex, cyclic, isogonal, equilateral, and diagonals are equal and perpendicular bisectors of each other.

Real-life Example

A few examples of squares are windows (unless they are rectangles), spaces on a chessboard, and keys on a keyboard.

1. Rhombus

According to the plane Euclidean geometry, a rhombus known as rhombi or rhombuses in plural form is a quadrilateral with four equal sides, i.e., all sides have the same length. As all sides of a rhombus are equal in length, its other name is ‘Equilateral Quadrilateral.’ Although appears as a special type of parallelogram and kite. In some cases, if a rhombus has right angles then it is a square.

Characterizations

Area: pq/2, where p and q are the diagonals of a rhombus

Perimeter: 4 x side of a rhombus

Number of Edges: Four (4)

Number of Vertices: Four (4)

Properties: Convex polygon, opposite angles are equal, and diagonals are congruent, perpendicular, and bisect each other as well as opposite angles.

Real-life Examples

Rhombus can be found as a kite, rhombus-shaped earring, mirrors, and even a section of the baseball field.

1. Kite

In Euclidean geometry, a kite is a 2D shape/quadrilateral whose four edges can be assorted into two pairs of equal sides that are adjacent to each other. A kite can be either convex or concave, but the term "kite" is often limited to the convex variety. Sometimes known as "dart" or "arrowhead," a concave kite is a type of pseudotriangle.

Characterizations

Area: ½ x product of the lengths of the diagonals

Perimeter: 2 x sum of lengths of the sides

Number of Vertices: Four (4)

Number of Edges: Four (4)