Properties of Rectangle
One of the most common geometrical figures that we see in our day-to-day 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 two-dimensional 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.
A square is a type of a rectangle with four equal sides and four equal angles. It is a two-dimensional 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.
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 vice-versa 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.
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.
Length of the rectangle = 14 cm; Width of a rectangle = 10 cm
Area of a rectangle: Length × Width
14 × 10 = 140 cm2
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?
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 inches2
Example 3: The perimeter of a rectangular pool is 86 meters. If the length of the pool is 40 meters, then find its width.
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 two-dimensional 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.