The name “parallelogram” comes from the Greek word “parallelogrammon,” which means “bounded by parallel lines.” As a result, a parallelogram is a quadrilateral with parallel lines on all sides. It’s a shape with parallel and equal sides on both sides. 

Parallelograms are divided into three types: square, rectangle, and rhombus, each with its own set of characteristics. We will learn about a parallelogram, how to find its area, and other elements of a parallelogram in this part, which will include solved problems.

Parallelogram

A quadrilateral formed by crossing lines is known as a parallelogram. The angle between adjacent sides of a parallelogram might vary, but the opposite sides must be parallel to be termed a parallelogram. A parallelogram is formed when the opposite sides of a quadrilateral are parallel and congruent.

As a result, a quadrilateral with parallel and equal opposite sides is known as a parallelogram.Properties of a Parallelogram

A parallelogram can be identified using a few fundamental properties. The following qualities can be used to identify and differentiate a parallelogram:

  • A parallelogram’s opposite sides are parallel. PQ || RT and PR || QT is used here.
  • A parallelogram’s opposite sides are equal. PQ = RT and PR = QT in this case.
  • A parallelogram’s opposite angles are equal. ∠P = ∠T and ∠Q = ∠R in this case.
  • A parallelogram’s diagonals cut each other in half. RE = EQ and PE = ET in this case.
  • Interior angles from the same side complement each other. ∠PRT + ∠RTQ = 180, ∠RTQ + ∠TQP = 180, ∠TQP + ∠QPR = 180, and ∠QPR + ∠PRT = 180, respectively.
  • The parallelogram is divided into two congruent triangles by the diagonals. ΔRPQ is equivalent to ΔQTR, and ΔRPT is equivalent to Δ

Types of Parallelogram

A parallelogram can be classified into several categories based on its distinct features. It is mostly separated into three distinct categories:

  • Rectangle
  • Square
  • Rhombus

Let’s take a closer look at these parallelograms.

Rectangle

A rectangle is a parallelogram with four right angles and two sets of opposite sides that are equal and parallel.                                            

A rectangle consists of:

  • There are two parallel sides. AB || DC and AD || BC is used here.
  • Four right angles Here, ∠A = ∠B = ∠C = ∠D = 90 and Opposite sides of equal length.  AB = DC and AD = BC in this case.
  • Two diagonals of equal length. AC = BD in this case.
  • Diagonals that bisect each other.

Square

A parallelogram with four equal sides and four right angles is known as a square.

A square consists of:

  • Four sides are equal. AB = BC = CD = DA in this case.
  • Four Right angles ∠A = ∠B = ∠C = ∠D = 90 in this case.
  • There are two parallel sides. AB || DC and AD || BC is used here.
  • Two diagonals of equal length. Diagonals that are perpendicular to each other, AC = BD ACBD Diagonals that cut each other in half or bisect it.

Rhombus

A rhombus is a parallelogram with four equal sides and opposite angles are equal.

A rhombus consists of:

  • There are two parallel sides. EH || FG and EF || HG  are used here.
  • Four sides are equal. EH = HG = GF= FE in this case.
  • Equal and oblique angles Diagonals that are perpendicular to each other are E = G and H = F in this case. EGHF Diagonals that cut each other in half.

Parallelogram Formulas

There are two basic formulas for every two-dimensional figure: area and perimeter. In this lesson, we’ll go through the two parallelogram formulas.

Area of Parallelogram

The space enclosed between the four sides of a parallelogram is known as its area. It may be computed using the base length and parallelogram height, and it is measured in square units like as cm2, m2, and inch2. 

Consider the PQRS parallelogram, which has a base (b) and a height (h). The area of a parallelogram can be determined using the formula: Area of Parallelogram = Base (b) Height (h)

Perimeter of Parallelogram

The perimeter of a parallelogram is equal to the sum of all its sides since it is the length of its outline.

P = 2 (a + b) units is the perimeter (P) of a parallelogram with sides.

Conclusion

A parallelogram is a flat shape having four straight, connected sides that are congruent and parallel on opposite sides. A parallelogram is a closed shape, a plane figure, and a quadrilateral.

Even if you possess practically all of these characteristics, you will not have a parallelogram. There is no closed shape if the four sides do not connect at their terminals; no parallelogram! You don’t have parallel sides if one side is longer than the other; you don’t have a parallelogram! You don’t have a parallelogram; you have a trapezoid if just one set of opposite sides is congruent.