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.
Different Types of Quadrilaterals
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.
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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).
Type: Quadrilateral.
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.
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°.
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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)
Type: Quadrilateral
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.
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.
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Characterizations
Area: Length × Width
Perimeter: 2 x (Length + Width)
Number of Vertices: Four (4)
Number of Edges: Four (4)
Internal Angles: All 90°
Type: Quadrilateral, Parallelogram, Hyperrectangle
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).
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.
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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.
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.
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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)
Type: Quadrilateral, parallelogram, and kite
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.
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.
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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)
Type: Quadrilateral
Line of Symmetry: 1
Rotational Symmetry: Order 1
Properties: Two pairs of congruent and consecutive sides, congruent non-vertex angles, and perpendicular diagonals.
Real-life Examples
Kite quadrilaterals are used for the wind-blown flying kites.
