The difference between a parallelogram and a rectangle is that a rectangle has two diagonals of equal length, while a parallelogram has two diagonals of unequal length. The opposite sides of a parallelogram are equal in length. Whereas if we talk about a rectangle, the opposite diagonals are not equal in length.

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## What is Parallelogram?

The opposite sides of a parallelogram are equal in length and the opposite angles are equal in measure. Additionally, the interior angles of the same side of the transversal are supplementary. The total sum of all the interior angles is 360 degrees.

### Properties of Parallelogram

**Opposite sides are parallel and equal**: The two pairs of opposite sides of a parallelogram are equal and have the same length.**Opposite angles are equal**: If you look at a parallelogram, the opposite angles are the same size.**Sum of Consecutive angles is 180 degrees**: The sum of two angles next to each other is 180 degrees.**All sides include a right angle**: If one angle in a parallelogram is a right angle (90 degrees), then all the other angles will also be right angles.**The two diagonals are exactly half**: If you draw the diagonals they cut each other exactly in half.**Each diagonal divides the parallelogram into two equal triangles**: Each diagonal divides the parallelogram into two pieces that are the same size and shape.**The sum of the squares of all sides equals the sum of the squares of its diagonals**: If you square the lengths of all the sides of a parallelogram and add them up, it will be the same as if you square the lengths of its diagonals and add them up. This is also called the parallelogram law.

## What is a Rectangle?

Height is generally the measurement of a shape in terms of its tallness. To measure the height of a particular shape the distance is measured from base to top. Sometimes, in geometry, it is also known as altitude. The height is generally measured for three-dimensional objects.

- Height is measured along the vertical axis on a graph.
- Height from the sea level is known as altitude.

### Properties of Rectangle

**Four sides and corners**: A rectangle has four sides and four corners where the sides meet.**Right angles at corners**: At each corner, the lines meet at a right angle**Equal and parallel opposite sides**: The sides opposite each other are the same length.**Diagonals cut each other in half**: The lines that connect opposite corners inside the rectangle cut each other exactly in the middle.**Perimeter is twice the sum of length and width**: If you add up the lengths of all four sides and then double that number, you get the total distance of the rectangle.**Area is length multiplied by width**: To find the space inside the rectangle, you can multiply the length by the width.**A rectangle is like a Square**: A rectangle is a special kind of parallelogram with right angles at all four corners.**All angles inside add up to 360 degrees**: If you add up all the angles inside the rectangle, you get 360 degrees.

## What is the Difference Between a Parallelogram and a Rectangle?

A rectangle has two diagonals of equal length and a parallelogram has two diagonals but of unequal length. In short, opposite sides of a parallelogram are equal in length. On the other hand, the opposite diagonals of the rectangle are not equal in length.

However, these two can seem to be confusing as it is often said that “** all rectangles are parallelograms but all parallelograms are not rectangles”**. Sometimes, there is confusion between these terms, to clear this confusion, you can get the difference between Parallelogram and Rectangle in the given table. Have a look at the table below.

Particulars | Parallelogram | Rectangle |

Definition | Length is a measurement of a shape in a straight line from end to end | Height measures a particular shape from its base to the top |

Angles | Opposite angles are equal | All angles are right angles |

Diagonals | Diagonals are not equal | Diagonals are equal |

Area | The area of parallelograms is bh (breadth x height) | The area of a rectangle is calculated by lw (length x width) |

Examples | A rhombus, a square, a rectangle with non-right angles | A sheet of paper, a door, a book |

## Parallelogram and Rectangle Formulas

Various Parallelogram and Rectangle formulas can be used to calculate the Parallelogram and Rectangle of a particular object. There are different scenarios when we talk about figuring out the area of Parallelogram, all of them are listed below.

- Area of Parallelogram Using Sides: Area = Base × Height
- Area of Parallelogram Without Height: Area = ab sin (x)
- Area of Parallelogram Using Diagonals: Area = ½ × d1 × d2 sin (y)

Particulars | Formulas to Find Area |

Using Base and Height | A = b × h |

Using Trigonometry | A = ab sin (x) |

Using Diagonals | A = ½ × d_{1} × d_{2} sin (y) |

The terms used in the above formulas can be described below:

b = base of the parallelogram (AB)

h = height of the parallelogram

a = side of the parallelogram (AD)

x = angle among the sides of the parallelogram (∠DAB or ∠ADC)

d1 = diagonal of the parallelogram (p)

d2 = diagonal of the parallelogram (q)

y = angle among the intersection point of the diagonals (∠DOA or ∠DOC)

### Formulas For Rectangle

Shape | Formula |

Perimeter of a Rectangle Formula | P = 2 (l + b) |

Area of a Rectangle Formula | A = l × b |

- In the Perimeter of a Rectangle Formula, the total distance around the rectangle. <br> P is the perimeter, l is the length, and b is the width.
- In the Area of a Rectangle Formula, the surface area of the rectangle. <br> A is the area, l is the length, and b is the width.

### Parallelogram vs Rectangle

Particulars | Parallelogram | Rectangle |

Area Formula | Area = Base × Height | Area = A = l × b |

Example | A parallelogram has a base length of 10 meters and a height of 8 meters. Calculate its area. If we put these figures in the formula: Area = Base × Height, We will get the result as the area of the parallelogram is 80. | If the length of the garden is 12 meters and the breadth is 8 meters, you can calculate the area of the garden by multiplying the length and breadth. The area of the garden would be 96 square meters.If we put these figures in the formula: Area = A = l × b, We will get the result as the area of the garden is 96. |

Practice Question | The area of a parallelogram is 210 square meters. If the base of the parallelogram measures 14 meters, what is the height of the parallelogram? | A rectangular swimming pool has a length of 25 meters and a breadth of 10 meters. What is the area of the pool? |

## Application of Parallelogram and Rectangle in Real Life

The tables that we use in daily life are often rectangular or square in design. A rectangle is made of two pairs of parallel, equal-length sides. Hence, the rectangle is also a parallelogram. As rectangular tables are a very common example of parallelogram-shaped things in everyday life.

## FAQ’s

**What is the area formula of Parallelogram?**

The area formula of Parallelogram is Area = Base × Height

**What is the area formula of a Rectangle?**

The area formula of the Parallelogram is Area = A = l × b

**All rectangles are parallelograms but all parallelograms are not rectangles, justify this statement.**

Rectangles have all the properties of parallelograms but all parallelograms do not have all the properties of rectangles:

– In a rectangle, all angles are right angles, whereas in a parallelogram, only opposite angles are equal.

– In a rectangle, the diagonals are of equal length, unlike in a parallelogram, where the diagonals are not necessarily equal.

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