What Is a Rectangle Definition Properties Formula and Examples
A rectangle in Euclidian geometry was put forward around 300 B.C. In plane geometry, the rectangle was held to be simply a quadrilateral having 4 right angles. Previously, it was also known as an equiangular quadrilateral. The present terminology is derived from the Latin word ‘rectangulus’ which can be divided into the components of ‘angulus’ which means angle and ‘rectus’ which means right.
Read on to know more about the definition of Rectangle and its other dimensions.
Rectangle Definition
In geometry, rectangle comprises of a 2D shape having four vertices and four sides and each angle measures 90°. It means that two sides always meet at right angles in a rectangle.
Moreover, sides facing each other are of the same lengths as well as parallel; that is, the distance between those two sides always remain the same at any given point. From rectangle definition, these characteristics are evident in the figure indicated below.
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Owing to the existence of parallel sides in a rectangle, it is termed as a parallelogram. Furthermore, it can also be an equiangular quadrilateral, given that all of its angles are equal.
Did you know?
All squares are rectangles, but not all rectangles are squares. Also, even though all parallelograms may not be rectangles but all rectangles are necessarily parallelograms. Interesting isn't it!
Formula of Rectangle
To define the area of a rectangle, its length and breadth are taken into consideration. It is the product of adjacent sides of a rectangle, that is, the product of its length and breadth. Hence, the area of a rectangle is,
[Where,
A = area of rectangle
l = length of rectangle
b = breadth of rectangle]
Similarly, the perimeter of a rectangle is the sum of its four sides. Therefore, the perimeter of a rectangle is,
[Where,
P = perimeter of rectangle
l = length of rectangle
b = breadth of rectangle]
The formula reflects that as the opposite sides of a rectangle are parallel, the rectangle’s perimeter would be two times the sum of length and breadth.
Properties of Rectangle
Proceeding from the rectangle definition, its main properties are –
All the angles are right-angled.
Opposite sides of a rectangle are congruent as well as parallel.
There is congruency in opposite angles which are created when two diagonals bisect.
Diagonals of a rectangle bisect each other, i.e., both are divided equally and congruent as well.
A rectangle is held to be a special instance of parallelogram comprising of right angles.
Solved Example
Here is an example, for better understanding of the definition of a rectangle –
What is the area and perimeter of a rectangle where the length and breadth are 15 cm and 11 cm respectively?
Given, length = 15 cm, breadth = 11 cm
Area of rectangle = (length × breadth) cm2 = (15 X 11) cm2 = 165 cm2
Perimeter of rectangle = 2 (length + breadth) = 2 (15 + 11) cm = 52 cm
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FAQs on Rectangle Definition and Key Properties Explained
1. What is a rectangle in geometry?
A rectangle is a four-sided polygon (quadrilateral) with four right angles (90° each) and opposite sides equal and parallel. In geometry, a rectangle has:
- Two pairs of equal opposite sides
- All interior angles equal to 90°
- Diagonals that are equal in length
2. What are the properties of a rectangle?
The main properties of a rectangle include equal opposite sides and four right angles. Key properties are:
- Opposite sides are equal and parallel
- All angles measure 90°
- Diagonals are equal and bisect each other
- Sum of interior angles is 360°
3. What is the formula for the area of a rectangle?
The area of a rectangle is calculated using the formula Area = length × width. In symbols:
- A = l × w
- If length = 8 cm and width = 5 cm
- Area = 8 × 5 = 40 cm²
4. What is the perimeter of a rectangle?
The perimeter of a rectangle is the total length of all four sides and is given by P = 2(l + w). Example:
- If length = 10 m and width = 4 m
- P = 2(10 + 4) = 2 × 14 = 28 m
5. How do you find the diagonal of a rectangle?
The diagonal of a rectangle is found using the Pythagoras theorem: d = √(l² + w²). Since a rectangle forms a right triangle with its sides:
- d² = l² + w²
- If l = 6 cm and w = 8 cm
- d = √(36 + 64) = √100 = 10 cm
6. What is the difference between a square and a rectangle?
The main difference is that a square has all four sides equal, while a rectangle has only opposite sides equal. Comparison:
- Rectangle: Opposite sides equal, all angles 90°
- Square: All four sides equal, all angles 90°
7. Is a rectangle a parallelogram?
Yes, a rectangle is a type of parallelogram because it has two pairs of parallel opposite sides. In addition to parallelogram properties, a rectangle also has:
- All angles equal to 90°
- Equal diagonals
8. What are the angles of a rectangle?
All four interior angles of a rectangle are 90°. Since the sum of angles in any quadrilateral is 360°:
- 90° + 90° + 90° + 90° = 360°
9. Can you give an example of a rectangle in real life?
Common real-life examples of a rectangle include objects with four right angles and opposite sides equal. Examples:
- Doors and windows
- Books and notebooks
- Mobile phone screens
- TV screens
10. How do you prove that a quadrilateral is a rectangle?
A quadrilateral is a rectangle if it has four right angles or if it is a parallelogram with one right angle and equal diagonals. You can prove it by checking:
- All angles are 90°, or
- Opposite sides are parallel and one angle is 90°, or
- Diagonals are equal and bisect each other
