Rectangle: Definition, Formula and Examples

What is a Rectangle?

A rectangle is one of the basic geometric shapes we learn about in maths. We can see many examples of a rectangle around us, like a notebook, a blackboard, a door, or a mobile phone's screen. So, what is a rectangle? A rectangle is a closed shape with four sides, where the opposite sides are equal and parallel, and all four corners are right angles (90°).

The longer side of a rectangle is called the length, and the shorter side is known as the breadth or width. These two sides help us find the perimeter and area of a rectangle using simple formulas. Learning about rectangles also helps us understand other geometric shapes and measurements better.

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Definition of a Rectangle

The definition of a rectangle states that it is a 2D closed shape with four sides, four corners, and four right angles. Each angle in a rectangle measures 90 degrees. The opposite sides of a rectangle are always equal and parallel to each other. The length and breadth of a rectangle help in finding its area and perimeter using different rectangle formulas.

What are the Length and Breadth of a Rectangle?

As we learnt, the length and breadth of a rectangle are its two main sides. The length is the longer side of the rectangle, while the breadth, also called width, is the shorter side. Both of these help in finding the area and perimeter of a rectangle.

When the area, perimeter, and one side of the rectangle are given, it becomes easy to find the other side using the rectangle formulas. For example, if you know the area and breadth, you can find the length by dividing the area by the breadth.

Read More: Area of Semicircle

Key Properties of a Rectangle

A rectangle has many key features that make it easy for you to identify it while solving maths problems in geometry. It is a four-sided quadrilateral shape where all the angles are right angles; that means each angle measures 90°. In addition to that, here are some important properties of a rectangle you should know:

• The opposite sides of a rectangle are equal and parallel.

• It has four right angles, and the sum of all angles is 360°.

• The diagonals of a rectangle are equal in length.

• The diagonals bisect each other, which means they cut each other into two equal parts.

• The diagonal of a rectangle can be found using Pythagoras' theorem:
  Diagonal = √(length² + breadth²)

• A rectangle is also a parallelogram, because its opposite sides are parallel. But not all parallelograms are rectangles because their angles are not always 90°.

Rectangle Formulas

In order to solve questions related to a rectangle, there are some rectangle formulas you need to remember. These formulas help you find the area, perimeter, length, and breadth of a rectangle easily.

• 1. Area of a Rectangle = Length × Breadth

• 2. Perimeter of a Rectangle = 2 × (Length + Breadth)

• 3. Length of a Rectangle = (Area ÷ Breadth) or (Perimeter ÷ 2) - Breadth

• 4. Breadth of a Rectangle = (Area ÷ Length) or (Perimeter ÷ 2) - Length

Also read:What is Hexagon?

Diagonal of a Rectangle

The diagonal of a rectangle is a line that joins the opposite corners of the rectangle. Every rectangle has two diagonals, and both are equal in length. When you draw a diagonal, it divides the rectangle into two right-angled triangles.

• In these triangles, the diagonal behaves as the hypotenuse, and the length and breadth of the rectangle become the other two sides.

• You can find the diagonal of a rectangle by using Pythagoras' theorem.

• If the length of the rectangle is l and the breadth is b, then the diagonal (d) can be found with this formula: Diagonal of a Rectangle (d) = √(l² + b²)

Read More: Lines and Angles

What is the Area of a Rectangle?

The area of a rectangle means the total space that the rectangle covers. For example, the flat surface of your notebook, a blackboard, or a laptop screen is all shaped like a rectangle. The space they cover is their area.

• The unit of area is always written in square units, such as cm², m², or inch², depending on the measurement used in the question.

• To find the area of a rectangle, you need to know its length and breadth. The formula is very simple: Area of a Rectangle = Length × Breadth

• For example, if the length of a rectangle is 4 cm and the breadth is 3 cm, then its area will be 4 × 3 = 12 square cm. 

Read More: (a + b)³ Formula

Perimeter of a Rectangle

The perimeter of a rectangle means the total distance around the outer boundary of the rectangle. In other words, it is the sum of all sides. With the length and breadth of a rectangle given, finding its perimeter becomes easy. The formula for the perimeter of a rectangle is:

• Perimeter of a Rectangle = 2 (Length + Breadth)

• The perimeter is always measured in linear units like centimetres (cm), metres (m), or inches (in).

• For example, if the length of a rectangle is 8 cm and the breadth is 4 cm, then its perimeter will be 2 × (8 + 4) = 24 cm. 

Types of Rectangles in Maths

A rectangle is a type of quadrilateral in which the opposite sides are equal, and each corner forms a right angle of 90°. The diagonals of a rectangle are also equal and can be found using the rectangle formulas.

Based on their side lengths and ratios, there are mainly two types of rectangles in maths: squares and golden rectangles. Let's learn about them one by one:

1. Square

A square is a special type of rectangle. In a square, all four sides are equal, and each angle is 90°. This means every square is a rectangle, but not every rectangle is a square. The flat surface of a chessboard or a tile is an example of a square.

2. Golden Rectangle

A golden rectangle is a rectangle in which the ratio of length to breadth follows the golden ratio (about 1 : 1.618). This type of rectangle is generally seen in art, design, and architecture because of its good-looking shape.

Also Read: Collinear Points

Solved Rectangle Examples

Here are some rectangle-related questions to help you understand how to use rectangle formulas like area, perimeter, and diagonal in real problems:

Example 1: Riya wants to put a lace around her rectangular photo frame. The length of the frame is 15 cm, and the breadth is 10 cm. How much lace will she need to cover the border?

Solution: Here, she needs to find the perimeter of the rectangle.
Perimeter = 2 (Length + Breadth)
= 2 (15 + 10)
= 2 × 25
= 50 cm

So, Riya will need 50 cm of lace to cover the frame.

Example 2: A rectangular garden has a length of 20 m and a breadth of 15 m. Find the area of the garden and the length of its diagonal.

Solution: Area = Length × Breadth = 20 × 15 = 300 m²

Now,
Diagonal (d) = √(l² + b²)
= √(20² + 15²)
= √(400 + 225)
= √625
= 25 m

So, the area of the garden is 300 m², and its diagonal is 25 m long.

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