What is a Rectangle?
Definition: Rectangle is a four sided polygon whose opposite sides are equal and all its angles measure 90°. The opposite sides of a rectangle are equal and parallel, and therefore, we can say that a rectangle is also a parallelogram.
The geometrical figure of a rectangle is as in the image.
In rectangle ABCD, sides AB and DC are equal in measurement and represent the length of the rectangle. Sides BC and DA are equal in measurement and represent the width of the rectangle. AC and BC are the diagonals of the rectangle and both the diagonals are equal in measurement. Additionally, all the adjacent sides are perpendicular to each other, which indicates that they make an angle of 90° at their intersection points or at the four vertices. Finally, the opposite sides AB and DC, BC and DA are parallel to each other.
Properties of a Rectangle
- It is a two dimensional four sided closed figure
- The opposite sides are parallel to each other
- The opposite sides are equal to each other
- Diagonals are equal in length
- Diagonals perpendicularly bisect each other
- Adjacent sides make a right angle at the vertex
- Perimeter of a rectangle is two times the sum of its length and width
- Area is the multiplication of the length and width
- The sum of all the interior angles as well as exterior angles is 360°.
Perimeter of a Rectangle
The perimeter of a rectangle is the distance covered by the outer surface of a rectangle. The perimeter of the following rectangle is calculated as,
Perimeter of rectangle = l + w + l + w
= 2 (l + w)
Perimeter of rectangle formula, Perimeter of rectangle calculator
Area of a Rectangle
The area of any two dimensional figure is the total space covered inside the boundaries of the figure. So, the area of a rectangle is the area covered by its boundaries.
Area of rectangle = l \( \times \) w
Read more on Area of a rectangle
Diagonals of a Rectangle
The diagonal of a 2-D figure is a line segment joining the opposite vertices of the figure. The diagonals of a rectangle are AC and BD. These diagonals can be calculated by using the Pythagorean theorem
Diagonal \( AC = BD = \sqrt{l^2 + w^2} \)
Rapid Recall
- A rectangle is a 2-D four sided closed figure whose opposite sides are parallel and equal to each other.
- Perimeter of rectangle = 2 (l + w)
- Area of rectangle = l \( \times \) w
- Diagonal \( AC = BD = \sqrt{l^2 + w^2} \)
Solved Examples on Rectangle
Example 1: Find the area of a rectangle if the length is 35 cm, and the width is 42 cm respectively.
Solution :
The length and width of a rectangle is 35 cm and 42 cm respectively.
Area of a rectangle = l \( \times \) w [Formula of area of rectangle]
= 35 \( \times \) 42 [Substitute the value]
= 1470 cm\( ^2 \).
So, the area of the rectangle is 1470 square centimeters.
Example 2: Sam walked around a rectangular park of 60 feet in width and 85 feet in length. He covered 7 rounds of this rectangular park. What is the total distance that Sam covered?
Solution:
The given dimensions of the rectangular park are 60 feet in width and 85 feet in length. The distance covered in one round is equal to the perimeter of the rectangular park.
Perimeter of rectangle = 2 (l + w) [Formula of perimeter of a rectangle]
= 2 (85 + 60) [Substitute the values]
= 290 feet
It is given that Sam covered 7 rounds.
So, total distance is 7 \( \times \) 290 = 2030 feet.
Example 3: Find the length of the diagonal of the rectangle in the image.
Solution:
The given rectangle is 8 m in length and 6 m in width.
Diagonal \( AC = \sqrt{l^2 + w^2} \) [Formula for the diagonal of a rectangle]
\( = \sqrt{8^2 + 6^2} \) [Substitute the value]
\( = 10 \) m
So, the diagonal of the given rectangle is 10 m in length.
The key difference between a square and a rectangle is that all the sides of a square are equal in length, but in a rectangle, only the opposite sides are equal in length.
A quadrilateral is a closed figure with four sides. So, a rectangle is a quadrilateral.
Yes, the diagonals of a rectangle are equal in length.
All the angles of rectangles are equal in measurement and equal 90 degrees.