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Rectangle Formula

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Rectangle belongs to the family of parallelograms, and parallelograms come under the types of quadrilaterals. The quality of a rectangle is that it has all its internal angles at 90°. The opposite sides of the rectangle are equal, however, the adjacent sides are not necessary to be equal. Let’s look at the formulae involved with the rectangle, for instance, the perimeter of the rectangle, the area of the rectangle, etc.

Area of a Rectangle

The area can be characterized as how much space is covered by a level surface of a specific shape. It is estimated as far as the “quantity of” square units (square centimetres, square inches, square feet, and so on) The area of a rectangle is the number of unit squares that can squeeze into a rectangle. A few instances of rectangular shapes are the level surfaces of PC screens, slates, blackboards, and so on.

Area of a Rectangle Formula

The equation of the area of a rectangle is utilized to observe the area involved by the rectangle inside its limit. The recipe for the area, ‘A’ of a rectangle whose length and width are ‘l’ and ‘w’ individually is the item “l × w”.

Area of a Rectangle = (Length × Breadth) square units.

Proof:

 

Area of Rectangle ABCD = Area of Triangle ABC + Area of Triangle ADC

= 2 × Area of Triangle ABC

= 2 × (1/2 × Base × Height)

= AB × BC

= Length × Breadth

Calculating Area of Rectangle

The area of a rectangle is equivalent to its length times its width. Follow the means referenced beneath to track down the area of a rectangle:

  1. Step 1: Note the components of length and breadth from the given information.
  2. Step 2: Find the result of length and breadth values.
  3. Step 3: Give the response in square units.

Area of a Rectangle by Diagonal

The diagonal of a rectangle is the straight line inside the rectangle interfacing its contrary vertices. There are two diagonals in the rectangle and both are of equivalent length. We can track down the diagonal of a rectangle by utilizing the Pythagoras theorem.

(Diagonal)2 = (Length)2 + (Breadth)2

(Length)2 = (Diagonal)2 – (Breadth)2

Length = √{(Diagonal)2 – (Breadth)2}

Now, the formula to calculate the area of a rectangle is Length × Breadth. Alternatively, we can write this formula as √{(Diagonal)2 – (Breadth)2} × Breadth.

Area of a Rectangle = Breadth (√{(Diagonal)2 – (Breadth)2}).

Perimeter of rectangle

Perimeter of a Rectangle could be considered one of the significant formulae of the rectangle. It is the absolute distance covered by the rectangle around its outside. In Maths, you will run over numerous mathematical shapes and sizes, which have a region, perimeter, and even volume (for three-dimensional figures). You will likewise gain proficiency with the equations for that large number of boundaries. A portion of the instances of various shapes are circle, square, polygon, quadrilateral, and so on In this article, you will concentrate on the vital element of the rectangle, for example, the perimeter.

Perimeter fundamentally gives the length of the figure. Assume for a square, which has every one of its sides as equivalent, the perimeter of the square will be multiple times its sides. On account of a circle, the perimeter is named as periphery, which is determined in light of its span. Before we figure out the perimeter of a given rectangle, let us learn first, what a rectangle is.

The perimeter of a rectangle is the complete distance covered by its limits or the sides. Since there are four sides of a rectangle, along these lines, the perimeter of the rectangle will be the amount of each of the four sides. Since the perimeter is a direct measure, accordingly, the unit of the perimeter of the rectangle will be in meters, centimetres, inches, feet, and so on.

Perimeter of a Rectangle Formula

Perimeter is nothing but boundary. In the above diagram, we have 4 sides. Adding those 4 sides we will get the perimeter of the rectangle. 

Sum of every side = L+ L+ B + B

So 2L+ 2B

Perimeter of rectangle = 2(L + B)

Applications of Perimeter of Rectangle

  1. We can decide the length of a rectangular field or a nursery for its fencing by utilizing the edge recipe
  2. It very well may be utilized for some craftsmanship and art undertakings, for example, embellishing the boundary of rectangular cardboard with vivid strips or ropes
  3. For the development of a rectangular pool, the length of swimming races are characterized by the edge
  4. For the development plan of the house, we want to define a limit utilizing substantial that is conceivable by the border equation

Sample Questions

Question 1: Find the area of the rectangle whose length is 21 units, width is 11 units.

Solution:

Given, length = 21 units and width = 11 units.

The formula to observe the area of a rectangle is A = length × breadth (l × b). 

Substitute 21 for ‘l’ and11 for ‘w’ in this equation. 

So, area of the rectangle = 21 × 11 = 231 sq units.

Question 2: Find the area of a rectangle of length of 12 mm and breadth of 8 mm.

Solution:

Length of a rectangle = 12 mm.

Breadth of a rectangle = 8 mm.

Area of a rectangle = length × breadth

= 12 × 8 sq mm.

= 96 sq mm.

Question 3: Finding the area of a rectangle whose length is 10.5 cm and breadth is 5.5 cm.

Solution:

Length of the rectangle (l) = 10.5 cm

Breadth of the rectangle (b) = 5.5 cm

Area of a rectangle = length × breadth (l × b)

Area of the rectangle = 10.5 × 5.5

= 57.75 cm2.

Question 4: The area of a rectangle is 32 cm2. If its breadth is 4 cm then find its length.

Solution:

Area of rectangle = 32 cm2

Breadth of rectangle = 4 cm

Length of rectangle = Area of the rectangle/Breadth of the rectangle

= 32 cm2/4 cm

= 8 cm.

So, the length of the rectangle is 8 cm.

Question 5: Find the perimeter of a rectangle whose length and width are 11 cm and 5.5 cm, respectively.

Solution:

Length = 11 cm and Width = 5.5 cm

The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(11 + 5.5) cm

P = 2 × 16.5 cm

Therefore, the perimeter of a rectangle = 33 cm.

Question 6: A rectangular yard has a length equal to 12 cm and a perimeter equal to 60 cm. Find its width.

Solution: 

Perimeter = 60 cm

Length = 10 cm

Let W be the width.

From the formula, 

Perimeter, P = 2(length + width)

Substituting the values, 

60 = 2(12 + width)

12 + W = 30

W = 30 – 12 = 18 

Hence, the width is 20cm.

Question 7: Find the perimeter of a rectangle whose length and width are 12cm and 4cm, respectively.

Solution:

Given,

Length = 12cm

Width = 4 cm

Perimeter of Rectangle = 2(Length + Width)

= 2(12 + 4) cm

= 2 × 16 cm

Therefore, the perimeter of a rectangle = 32 cm.

Question 8: Find the perimeter of a rectangle whose length is 21 cm and width is 13 cm.

Solution:

Given,

Length = 21cm

Width = 13 cm

Perimeter of Rectangle = 2(Length + Width)

= 2(21 + 13) cm

= 2 × 34 cm

Therefore, the perimeter of a rectangle = 68cm.



Last Updated : 10 Jan, 2024
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