Rectangle

In geometry, understanding different shapes is essential. One of the most common and recognizable shapes is the rectangle. You can find rectangles in many everyday items, such as blackboards, books, tables, and phone screens.  

This guide will help you learn about rectangles, including their definition, shape, real-life examples, key properties, and formulas for calculating area, perimeter, and diagonal length using the Pythagorean theorem. With clear explanations and examples, this guide makes learning about rectangles simple and enjoyable.  

 

Table of Contents

• Definition
• Shape of Rectangle
• Rectangular Shaped Objects (Real-Life Examples)
• Properties of Rectangle
• Perimeter of Rectangle
• Area of Rectangle
• Diagonal of Rectangle
• Length of Diagonals
• Solved Examples
• Conclusion
• Frequently Asked Questions on Rectangles

 

Definition  

A rectangle is a four-sided polygon, also called a quadrilateral, with each interior angle measuring exactly 90 degrees. In simple terms, a rectangle is a type of parallelogram where opposite sides are equal in length, and each angle is a right angle.  

This makes rectangles one of the most common shapes in mathematics and everyday life. Due to its unique combination of equal angles and equal opposite sides, the rectangle belongs to the category of special quadrilaterals.  

 

Shape of Rectangle  

The shape of a rectangle is distinctive. It has:  

• Four sides (a quadrilateral)  

• Four right angles (each 90 degrees)  

• Two pairs of equal and parallel opposite sides  

Unlike a square, where all four sides are equal, a rectangle has only its opposite sides equal. This results in different lengths and widths, giving rectangles a more elongated or stretched look.  

This shape makes rectangles versatile and suitable for practical use in engineering, art, and design.  

 

Rectangular Shaped Objects  

You encounter rectangular objects every day. Their practical design and mathematical properties make them efficient in various fields. Common examples of rectangular objects include:  

• Mobile phones  

• Notebooks  

• Television and computer screens  

• Windows and doors  

• Tables, whiteboards, and bricks  

• Sheets of paper (A4, letter-size, etc.)  

The design of these rectangular items is based on the properties of rectangles, particularly their ease of stacking, organizing, and dividing space evenly.  

 

Properties of Rectangle  

Understanding the properties of rectangles is critical in geometry. These properties assist in identifying, calculating, and working with rectangles.  

• All angles are right angles (90° each).  

• Opposite sides are equal and parallel.  

• The diagonals are equal in length.  

• Each diagonal bisects the rectangle, creating two congruent right triangles.  

• The area of  rectangle is found by multiplying its length and width.  

• The Perimeter of  Rectangle is twice the sum of its length and width.  

 

These properties make rectangles predictable and easy to work with in various mathematical and physical applications.  

 

Perimeter of  Rectangle  

The Perimeter of  Rectangle is the total distance around its outer boundary. It is a fundamental measurement when outlining space or enclosing an area.  

Perimeter of Rectangle Formula:  

Perimeter = 2 × (Length + Width)  

Example:  

If a rectangle has a length of 10 cm and a width of 5 cm:  

Perimeter = 2 × (10 + 5) = 2 × 15 = 30 cm  

 

The Perimeter of  Rectangle is useful for:  

• Fencing rectangular plots  

• Framing photos or art  

• Determining borders or boundaries  

Once the properties of rectangles are understood, repeating this calculation becomes intuitive.  

 

Area of Rectangle  

The area of  rectangle measures the space enclosed within its four sides. It indicates how much surface the rectangle covers.  

Area of Rectangle Formula:  

Area = Length × Width  

This formula is simple yet powerful, making it one of the most commonly used in geometry.  

 

Example:  

If a rectangle has a length of 8 meters and a width of 3 meters:  

Area = 8 × 3 = 24 square meters  

 

You will find the area of  rectangle useful for:  

• Flooring and tiling work  

• Designing gardens  

• Arranging seating layouts  

• Painting or wallpapering walls  

Calculating the area of  rectangle is straightforward and essential for real-world problems due to the properties of rectangles.  

 

Diagonal of  Rectangle    

The Diagonal of  Rectangle   is the straight line segment connecting two opposite corners (vertices). Each rectangle has two diagonals, both equal in length because of the symmetry and properties of rectangles.  

Diagonal of Rectangle Formula:  

Using the Pythagorean theorem, the diagonal can be calculated as:  

Diagonal = √(Length² + Width²)  

 

Example:  

For a rectangle with a length of 6 units and a width of 8 units:  

Diagonal = √(6² + 8²) = √(36 + 64) = √100 = 10 units  

 

Understanding the Diagonal of  Rectangle   is important for:  

• Construction of rectangular structures  

• Designing screens and display areas  

• Diagonal bracing in engineering  

This diagonal divides the rectangle into two congruent right triangles due to the properties of rectangles.  

 

Length of Diagonals  

As mentioned, the length of diagonals in a rectangle is the same for both diagonals. You can find the length of the diagonals using:  

Length of Diagonals = √(Length² + Width²)  

 

This comes from the triangle formed when a diagonal splits the rectangle. The diagonal length is important when:  

• Creating symmetrical designs  

• Checking if an object is perfectly rectangular  

• Installing tiles or cutting boards diagonally  

Knowing the length of the diagonals ensures that a rectangle is properly constructed and balanced.  

 

Solved Example  

Let’s apply the concepts of area, perimeter, and diagonal together in one problem.  

 

Example 1: Find the area of  rectangle  

Question:  

Find the area of  rectangle with a length of 12 cm and a width of 8 cm.  

Solution:  

area of  rectangle = Length × Width  

Area = 12 cm × 8 cm = 96 cm²  

Answer: 96 cm²  

 

Example 2: Find the Perimeter of  Rectangle  

Question:  

Calculate the Perimeter of  Rectangle with a length of 15 cm and a width of 10 cm.  

Solution:  

Perimeter of  Rectangle = 2 × (Length + Width)  

Perimeter = 2 × (15 + 10) = 2 × 25 = 50 cm  

Answer: 50 cm  

 

Example 3: Find the Length When Area and Width Are Given  

Question:  

The area of rectangle is 120 cm², and its width is 10 cm. Find its length.  

Solution:  

Area = Length × Width  

120 = Length × 10  

Length = 120 ÷ 10 = 12 cm  

Answer: 12 cm  

 

Example 4: Determine Width Using Perimeter and Length  

Question:  

The Perimeter of  Rectangle is 60 cm, and the length is 18 cm. Find the width.  

Solution:  

Perimeter = 2 × (Length + Width)  

60 = 2 × (18 + Width)  

30 = 18 + Width  

Width = 30 - 18 = 12 cm  

Answer: 12 cm  

 

Example 5: Diagonal of  Rectangle    

Question:  

A rectangle has a length of 9 cm and a width of 12 cm. Find the length of its diagonal.  

Solution:  

Using the Pythagorean theorem:  

Diagonal = √(Length² + Width²)  

= √(9² + 12²) = √(81 + 144) = √225 = 15 cm  

Answer: 15 cm  

 

Conclusion  

The rectangle is more than just a common geometric shape. It is an important structure in both academic and real-world contexts. With clearly defined properties and formulas for calculating area, perimeter, and diagonal length, the rectangle becomes a fundamental topic in geometry.  

Whether solving math problems or measuring rectangular objects, understanding rectangles is always beneficial. Memorizing the area formula and other key concepts ensures success in schoolwork, construction, design, and more.  

 

Frequently Asked Questions on Rectangles

1. Which shape is a rectangle?

Ans: A rectangle is a quadrilateral (four-sided shape) where opposite sides are equal and parallel, and all four angles are right angles (90 degrees). It is a type of parallelogram.

 

2. How many sides are in a rectangle?

Ans: A rectangle has 4 sides. Opposite sides are equal in length and parallel to each other.

 

3. What is the definition of a rectangle?

Ans: A rectangle is defined as a four-sided polygon (quadrilateral) in which each angle is 90 degrees and opposite sides are equal and parallel. The diagonals of a rectangle are also equal in length.

 

4. What is the rectangle of 4?

Ans: The phrase "rectangle of 4" is unclear or incomplete. However, if it refers to a rectangle with side lengths related to the number 4, for example:

• A rectangle with length = 4 units and width = 2 units
  Then,

• Area = length × width = 4 × 2 = 8 square units

 

Keep learning and practicing Rectangle concepts with Orchids The International School to master geometry easily.