Rectangle - Definition, Properties, and Formulas

The concept of rectangle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. From classroom geometry to daily objects like books, screens, and tables, the rectangle is one of the most recognized shapes. Let’s understand its definition, properties, formulas, and how to solve rectangle problems easily.

What Is Rectangle?

A rectangle is a four-sided polygon (quadrilateral) with opposite sides equal and all four interior angles exactly 90 degrees. You’ll find this concept applied in measurement, geometry problems, and practical design scenarios. Many basic objects like an A4 sheet, blackboard, TV screen, and mobile phone are in the shape of a rectangle, making it an important foundation in maths education.

Key Formula for Rectangle

Here are the standard formulas for a rectangle:

• Area of Rectangle: \( A = L \times W \)
  (where L = length, W = width or breadth)
• Perimeter of Rectangle: \( P = 2 (L + W) \)
• Diagonal of Rectangle: \( D = \sqrt{L^2 + W^2} \)

Properties of Rectangle

1. All four angles are right angles (each is 90°).
2. Opposite sides are equal and parallel.
3. Both diagonals are equal in length.
4. The diagonals bisect each other (they cross at the center).
5. A rectangle is a special parallelogram with all angles equal.
6. The sum of the interior angles is always 360°.
7. A rectangle has two lines of symmetry.

Difference Between Rectangle and Square

Rectangle	Square
Opposite sides equal, adjacent sides can differ	All four sides equal in length
All angles are 90°	All angles are 90°
Diagonals equal and bisect each other	Diagonals equal, bisect each other at right angle (90°)
2 lines of symmetry	4 lines of symmetry

Step-by-Step Illustration

Let’s solve a typical rectangle problem:

Question: The sides of a rectangle are 5 cm and 12 cm. Find the area, perimeter, and length of the diagonals.

1. Given: Length (L) = 5 cm, Width (W) = 12 cm

2. Area: \( A = L \times W = 5 \times 12 = 60\ \mathrm{cm}^2 \)

3. Perimeter: \( P = 2(L + W) = 2(5 + 12) = 2 \times 17 = 34\ \mathrm{cm} \)

4. Diagonal: \( D = \sqrt{L^2 + W^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13\ \mathrm{cm} \)

Final Answers: Area = 60 cm², Perimeter = 34 cm, Diagonal = 13 cm.

Speed Trick or Vedic Shortcut

A rapid way to find if a quadrilateral is a rectangle is to check if it has one right angle and its diagonals are equal. You don’t need to check all angles every time in competitive exams. Remember, for unknown side problems, rearrange the area or perimeter formula to solve quickly!

Example Trick: If area and length are given, you can instantly find width by \( W = \frac{A}{L} \).

Vedantu teachers often share more such tips to boost your maths speed and accuracy.

Try These Yourself

• Find the area and perimeter of a rectangle with length 7 cm and width 9 cm.
• If the diagonal is 10 cm and length is 6 cm, what is the width?
• List three daily-life objects that are rectangles.
• Explain why a square is a type of rectangle.

Frequent Errors and Misunderstandings

• Mixing up length and width (always label clearly).
• Using wrong units (area is in square units, perimeter is in regular units).
• Forgetting to double while calculating perimeter (2 × (L + W)).
• Assuming a rectangle and parallelogram are always the same (but only rectangles have all right angles).

Relation to Other Concepts

The idea of rectangle connects closely with quadrilaterals and parallelograms. Mastering rectangles helps with understanding area, perimeter, symmetry, and other two-dimensional shapes in further chapters.

Classroom Tip

A quick way to remember rectangle properties: “Opposite sides are equal, all angles are right, and diagonals cross at the center.” Drawing and labeling rectangles regularly in your notebook will help fix the formulas in your mind. Vedantu’s live classes often use practical objects like books and screens to make this more visual for students.

Real-Life Examples of Rectangle

• Book covers
• Mobile phone screens
• Doors and windows
• A4 size sheets and envelopes
• Television and monitor displays

Rectangle in Other Subjects

Rectangle is not only useful in Maths but also vital in Physics (area calculations), Computer Science (grid layouts), Engineering and daily logic puzzles. Students preparing for JEE, NEET, and Olympiads will regularly encounter rectangles in geometry and mensuration questions.

We explored rectangle—from its definition, formulas, properties, example problems, mistakes to avoid, and connections to other mathematical topics. Continue practicing with Vedantu for deeper understanding and exam success!

You may also like: Area of Rectangle | Perimeter of Rectangle | Properties of Rectangle | Difference Between Square and Rectangle