Properties of Rectangle
One of the most common geometrical figures that we see in our daytoday life is a rectangle. It is an equiangular quadrilateral in which the opposite sides are parallel and equal to each other and all four angles are right angles. The longer side of a rectangle is called its length and the shorter side is the width.
1.  What is a Rectangle? 
2.  Types of Rectangles 
3.  Properties of a Rectangle 
4.  Formulas of a Rectangle 
7.  FAQs on Properties of Rectangle 
What is a Rectangle?
A rectangle is a twodimensional figure with four sides, four vertices, and four angles. The opposite sides of a rectangle are equal in length and are parallel to each other. Since a rectangle is a quadrilateral in which all four angles are equal to each other, the angle formed by its adjacent sides is 90°. The four sides of a rectangle are not equal AND a rectangle cannot be a square, although a square can be a rectangle. Some of the examples we see in daily life in the shape of a rectangle are a kite, paintings, slabs, a storage box, etc.
Types of Rectangles
A rectangle has four sides with the opposite sides equal to each other and with the adjacent sides meeting at 90°. These properties are seen in the two types of rectangles  the Square and the Golden Rectangle.
Square
A square is a type of a rectangle with four equal sides and four equal angles. It is a twodimensional shape where the interior angles at each vertex are 90°. Along with these properties, the opposite sides of a square are equal and parallel and the diagonals bisect each other at 90°. It can be said that all squares are rectangles but all rectangles cannot be squares.
Golden Rectangle
The golden rectangle is a rectangle whose sides are in the golden ratio, that is, (a + b)/a = a/b, where 'a' is the width and (a +b) is the length of the rectangle. In other words, a golden rectangle is a rectangle whose 'length to width ratio' is similar to the golden ratio, 1: (1+⎷ 5)/2. For example, if the length is around 1 foot long then the width will be 1.168 feet long or viceversa where the Golden Ratio = 1: 1.618. Observe the following figure which shows the golden rectangle and its length and width.
Properties of a Rectangle
In order to understand the rectangle better, let us look at the vast properties that a rectangle has.
 A rectangle is a quadrilateral with four equal interior angles.
 The opposite sides of a rectangle are equal and parallel to each other.
 The interior angle of a rectangle at each vertex measures 90°.
 The sum of all interior angles is 360°.
 The diagonals bisect each other  one obtuse angle and the other an acute angle.
 The length of the diagonals is equal.
 The length of the diagonals can be obtained using the Pythagoras theorem. The length of the diagonal with sides a and b is √( a² + b²).
 Since the sides of a rectangle are parallel, it is also called a parallelogram.
 All rectangles are parallelograms but all parallelograms are not rectangles.
 When two diagonals bisect each other at 90° it is called a square.
Formulas of a Rectangle
While solving problems related to rectangles, there are three main formulas to remember. They are related to the area of a rectangle, the perimeter of a rectangle, and the length of the diagonal.
Area of a Rectangle: A = l × w, where 'l' and 'w' are the length and width of the rectangle, respectively.
The perimeter of a Rectangle: P = 2(l + w), where 'l' is the length and 'w' is the width of the rectangle.
The formula for the diagonal of a rectangle is derived from the Pythagoras theorem.
Diagonal of Rectangle (d) = √(l² + w²), where 'l' is the length and 'w' is the width of the rectangle.
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Solved Examples

Example 1: If the length and width of a rectangle are 14 cm and 10 cm, respectively, Calculate the area and perimeter of the rectangle.
Solution:
Length of the rectangle = 14 cm; Width of a rectangle = 10 cm
Area of a rectangle: Length × Width
14 × 10 = 140 cm^{2}
Perimeter of a rectangle = 2 (length + width)
2 (14 + 10) = 24 × 2 = 48 cm

Example 2: George has a rectangular photo frame that is 11 inches long and 8 inches wide. Can you help George find its area?
Solution:
Area of a Rectangle = (Length × Width). Thus, the area of the rectangular frame = 11 × 8 = 88 square inches
Therefore, the area of the photo frame = 88 inches^{2}

Example 3: The perimeter of a rectangular pool is 86 meters. If the length of the pool is 40 meters, then find its width.
Solution:
The formula to calculate the perimeter is P = 2 (length + width)
Given that, the perimeter is 86 meters and the length is 40 meters. Substituting these values into the formula.
86 = 2(40 + w)
86 = 80 + 2w
6 = 2w
w = 3
Therefore, the width of the rectangular pool is 3 meters.
FAQs on Properties of Rectangle
What is a Rectangle?
A rectangle is a twodimensional shape with four sides, four angles, and four vertices. The opposite sides of a rectangle are equal and parallel to each other. The interior angles of a rectangle are equal and measure 90°.
What are the Properties of a Rectangle?
The basic properties of a rectangle are that its opposite sides are parallel and equal and its interior angles are equal to 90°. Its diagonals are also equal and they bisect each other.
Is a Square a Rectangle?
Yes, a square is considered as a rectangle as it contains the properties of a rectangle, like, all the four interior angles are 90°, the opposites sides of a square are parallel and equal to each other, and two diagonals of the square are equal and bisect each other.
What is the Difference Between a Square and a Rectangle?
Squares have some additional properties which do not apply to rectangles. A square has all four sides equal, whereas, in a rectangle, only the opposite sides are equal.
What are the Various Types of Quadrilaterals other than Rectangles?
The various types of quadrilaterals other than rectangle are squares, rhombus, kite, parallelogram, and a trapezoid.
Why is a Rectangle not a Square?
A rectangle does not have all four sides of equal measure. This is the reason that a rectangle is not a square.