Quadrilaterals-Rectangle

The rectangle is an essential topic in the domain of mathematics. It comes under the category of the quadrilateral. In the numeric world, quadrilaterals are explained as a polygon of four sides. It also has four corners known as vertices. The term is derived from the Latin root word “Quadri” and “latus” which means any variation that has four sides in it. 

Matching the essential features of a rectangle to that of a quadrilateral, it becomes easy to identify and vindicate that both of the figures have the same trait and features. The rectangle is 2D in shape and the two opposite sides are equal in length and each side angle measures at 90°.

Explain Rectangle in details

A rectangle is an essential part of the subject of mathematics. This is a kind of quadrilateral that has many important aspects from the point of view of researchers and academicians. A quadrilateral is any given shape that has four edges and four vertices. This rectangle has two equal opposite sides in length. 

The angles of the rectangle are 90°. The diagonals are drawn inside the rectangle connect two opposite corners of the given rectangle. Thus, in total, two diagonals can be drawn, inside a given rectangle. 

These diagonals cut each other in halves. The angles formed by the intersection of the two diagonals are not always equal. The rectangle is also sometimes referred to as a tetragon, which means any shape made of four sides. 

The above-given figure “abab” represents a rectangle. The opposite sides are always equal to each other. The angles are shown to be at 90°. The diagonal D is also depicted as connecting two opposite corners of the rectangle “abab”.

The rectangle also defines an equi-angular quadrilateral since all the angels are exactly at 90°. The summation of all angles of a rectangle is 360°.

Explain various properties of a rectangle

The rectangle has various properties that segregate it from different other shapes in the field of mathematics. The various properties of a rectangle are angles of equal measurement that are each measured at 90°, hence they are equiangular. The opposite sides of a rectangle are equal in length; these sides are also parallel to each other. 

The sum of all the interior angles of a rectangle is equal to 360°. The diagonals of a given rectangle bisect each other. The diagonal cut to either diagonal at halves and the angle formed is 90°. The length of the given diagonal like that in the figure is always equal. 

The length of a diagonal can be obtained by using the theory propounded by “Pythagoras”. For any given side m and n, the theorem would be √(m2+n2). The rectangle can be also categorized under the definition of a parallelogram as the opposite sides are parallel to each other. 

All types of rectangles come under the broad definition of a parallelogram. However, there are a few kinds of parallelograms that are not rectangles from the point of mathematics. The rectangle with two sides j, k  has a perimeter that is measured with the formula 2j+2k units, the area will be measured with the formula length x breadth.

The longer slide of a rectangle is termed as length, and the shorter side is termed as breadth. 

State rectangle definition

A rectangle definition is any given shape in the field of mathematics that has four sides; however, the opposite sides are equal to each other. The longer side is called the length and the relatively shorter side is termed the breadth. 

The rectangle has the features of both a quadrilateral and a parallelogram. It is a parallelogram because the two opposite sides are parallel, in comparison to the other. A rectangle is of different kinds depending on the feature it possesses. 

A Cross rectangle is a type of rectangle that self-intersects itself. There exist two opposite sides along the diagonals of the rectangle. A golden rectangle is a rectangle whose sides are in the golden ratio.

Enlist various formulas of rectangles

There are various important formulas for calculation about a rectangle.

The area of a rectangle with side f and m is measured with the formula f x m.

The perimeter of the rectangle is calculated with the formula 2( f+m), in the above rectangle with sides f and m. The diagonal of the rectangle is measured with the formula (f2+m2). The length (f) is contained in the area formula by area/ m. The breadth (m) is also obtained by the formula area/ f.

Conclusion 

The rectangle is an important part of the subject of mathematics. The researchers are using the vital features of rectangles for various purposes. The rectangle is a type of quadrilateral. A quadrilateral is a type of polygon with four sides. It also has four different corners.