Properties of Rectangle

What is Rectangle?

A rectangle is a four-sided two-dimensional plane figure. A rectangle is a four-sided polygon with opposing sides that are parallel and equal in length. It is one of the types of quadrilateral in which all four angles are right angles or equal to 90 degrees. A rectangle is a type of parallelogram in which all of the angles are equal. A square is defined as a rectangle having four equal sides. Now let us learn what are the properties of a rectangle in this article.


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Characteristics of a Rectangle

A rectangle is defined by its length (L) and width (W) (W). Both the length and the width are scaled differently. A rectangle ABCD has four sides AB, BC, CD, and DA, as well as right angles A, B, C, and D, as seen in the diagram. The length (L) of the distance between A and B or C and D is defined as the length (L) of the given rectangle, while the width (W) of the given rectangle is defined as the distance between B and C or A and D.


Shape of Rectangle

A rectangle is a two-dimensional flat shape of two dimensions. We can easily represent a rectangle in an XY plane by using the arms of the x-axis and the y-axis to indicate the length and width of the rectangle, respectively.


Rectangular Shaped Objects

Televisions, computer screens, notebooks, cell phones, CPUs, notice boards, tables, books, TV screens, mobile phones, walls, magazines, tennis courts, and so on are some of the most popular rectangular everyday items we see.


Properties of Square and Rectangle

Here we have listed the Properties of square and rectangle


Properties of a Square

The following are the most important properties of a square:

  • All four interior angles are equal to 90°

  • The square's four sides are congruent or equal to one another.

  • The square's opposite sides are parallel to each other.

  • The square's diagonals are 90 degrees apart and bisect each other.

  • The square's two diagonals are identical in length.

  • The square has four sides and four vertices.

  • The square's diagonal divides it into two identical isosceles triangles.

  • The length of the diagonals exceeds the length of the square's sides.


Fundamental properties of rectangle

If you want to write the properties of rectangle, then take a look at the following pointers to gain a better understanding. 

  • A quadrilateral is a rectangle.

  • Each interior angle is 90 degrees and the opposite sides are parallel and equal to each other.

  • The sum of all the interior angles is equal to 360 degrees

  • The diagonals are parallel to each other and have the same length.

  • The perimeter of a rectangle with side lengths a and b is 2a+2b units.

  • The area of a rectangle with side lengths a and b is ab sin 90 = ab square units.

  • The diameter of a rectangle's circumcircle is its diagonal.

  • If a and b are the sides of a rectangle, then the length of each diagonal is: \[d=\sqrt{a^{2}+b^{2}}\]

  • The diagonals bisect each other at different angles. One is an acute angle, and the other is an obtuse angle.

  • The rectangle is known as a square if the two diagonals bisect each other at right angles.

  • When the rectangle is rotated along the line connecting the midpoints of the longer parallel sides, it forms a cylinder. The height of the cylinder is equal to the width of a rectangle in this situation. In addition, the diameter of a cylinder is equal to the length of a rectangle.

  • When the rectangle is rotated along the line connecting the midpoints of the shorter parallel sides, the result is a cylinder. In this case, the cylinder's height is equal to the rectangle's length. Similarly, the width of a rectangle is equal to the diameter of a cylinder.


In the above point, we have discussed all properties of rectangles. Students should know all these properties.


Perimeter of a Rectangle

The diameter of a rectangle is the cumulative distance protected by the rectangle's outer boundary. It is counted in units of time. The perimeter formula is as follows:

Perimeter, P = 2 (Length + Width) 


Area of Rectangle

The region covered by a two-dimensional shape in a plane is called the area. It is based on square units of measurement. As a result, the rectangle's area is equal to the area enclosed by its outer boundaries. It equals the sum of the length and width.

The formula of area of rectangle is:

A = Length x Width  units2


Length of Diagonals of Rectangle

The rectangle is a symmetrical shape with equal length diagonals on both sides. The rectangle will be divided into two right-angle triangles by a diagonal. As a result, the Pythagorean Theorem can be used to conveniently measure the length of diagonals, where the diagonals are treated as the right triangle's hypotenuse.


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Let D be the hypotenuse, and L and W, respectively, be the base and perpendicular. As a result, the rectangle's diagonal length would be:

\[d=\sqrt{L^{2}+W^{2}}\]


Solved Examples

1. Calculate the Circumference of a Rectangle With Sides of 10cm and 5cm.

Solution:

Given:

a = 10 cm

b = 5 cm

According to the properties of a rectangle, we know that the perimeter of a rectangle is:

Perimeter, P = 2a +2b units

P =2(a+b) units

Now, substitute the values

P=2(10+5)

P=2(15)

P=30 cm

Hence, the perimeter of a rectangle is 30 cm.


2. Find the Length of the Diagonal of a Rectangle Where Length and Width Are Given as 12 and 9 Cm Respectively.

Sol: Given length =12 cm and width = 9cm

We know the diagonal formula \[d=\sqrt{L^{2}+W^{2}}\]

\[\Rightarrow d=\sqrt{12^{2}+9^{2}}\]

\[\Rightarrow d=\sqrt{144+81}\]

\[\Rightarrow d=\sqrt{225}\]

\[\Rightarrow d= 15cm\]

Hence length of diagonal = 15cm.


Conclusion

In this article, we have learnt the definition of a rectangle and its properties. We can conclude that all squares are rectangles, but not all rectangles are squares. Since it has all of the properties of a rectangle, a square is a special type of rectangle. We know what are the properties of a rectangle and also we have solved a few example problems.

FAQs (Frequently Asked Questions)

1. What is the Shape of a Rectangle?

Ans: A rectangle is a closed flat shape with four sides and angles of 90 degrees on each side. The rectangle's opposite sides are identical and parallel.

2. What is the Difference Between a Rectangle and a Square?

Ans: Both the rectangle and the square have four sides and four internal angles and are closed geometrical figures (each angle measuring 90 degrees). The four sides of a square are all the same length. The adjacent sides of a rectangle, on the other hand, have different lengths. The opposing sides are on a level playing field.

3. Define the Shape of Square.

Ans: A square is a four-sided polygon with all four sides equal in length and all angles measuring 90 degrees. The square's form is such that if a plane is sliced through it from the middle, both halves are symmetrical. Each half of the square now resembles a rectangle with equal sides on both sides.