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 necessarily equal.
Table of Content
Rectangle Formulas
For a Rectangle ABCD with length(l) and breadth(b), various formulas used to solve problems of rectangles are:
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A = l.b sq units |
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P = 2(l + b) units |
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Diagonal of Rectangle Formula |
d = √(l2 + b2) unit |
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 = (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
Follow the steps added below to calculate Area of Rectangle
Step 1: Note the components of length and breadth from the given information.
Step 2: Find the result of length and breadth values.
Step 3: Give the response in square units.
Area of a Rectangle by Diagonal
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 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
Perimeter of Rectangle = 2(L + B)
Examples on Rectangle Formulas
Example 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
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 rectangle = 21 × 11 = 231 sq units
Example 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
Example 3: Finding the area of a rectangle whose length is 10.5 cm and breadth is 5.5 cm.
Solution:
Length of rectangle (l) = 10.5 cm
Breadth of rectangle (b) = 5.5 cm
Area of a rectangle = length × breadth (l × b)
Area of rectangle = 10.5 × 5.5
= 57.75 cm2
Example 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.
Example 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
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.
Example 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.
Example 7: Find the perimeter of a rectangle whose length and width are 12cm and 4cm, respectively.
Solution:
Given,
Length = 12 cm
Width = 4 cm
Perimeter of Rectangle = 2(Length + Width)
= 2(12 + 4) cm
= 2 × 16 cm
Therefore, the perimeter of a rectangle = 32 cm.
Example 8: Find the perimeter of a rectangle whose length is 21 cm and width is 13 cm.
Solution:
Given,
Length = 21 cm
Width = 13 cm
Perimeter of Rectangle = 2(Length + Width)
= 2(21 + 13) cm
= 2 × 34 cm
Therefore, the perimeter of a rectangle = 68 cm.
Practice Questions on Rectangle Formulas
Q1. Find the area of a rectangle with length 8 units and width 5 units.
Q2. Determine the perimeter of a rectangle with length 12 units and width 6 units.
Q3. If the area of a rectangle is 48 square units and its length is 8 units, what is its width?
Q4. Given that the perimeter of a rectangle is 40 units and its length is 12 units, what is its width?
Q5. A rectangle has a diagonal of length 10 units. If its length is 6 units, what is its width?
Q6. Calculate the length of the diagonal of a rectangle with length 9 units and width 12 units.
Q7. If the perimeter of a rectangle is 60 units and its width is 8 units, what is its length?
Q8. A rectangle has an area of 72 square units. If its width is 6 units, what is its length?
Q9. Find the length of a rectangle with a perimeter of 28 units and a width of 5 units.
Q10. If the length of a rectangle is x + 4 units and its width is x – 2 units, express the area of the rectangle in terms of x
FAQs on Rectangle Formulas
What is the formula for the area of a rectangle?
Area of rectangle is space occupied by the boundaries of the rectangle and is calculated by the formula: A = l.b sq units.
What is the formula for the perimeter of a rectangle?
Perimeter of rectange is the length of all the boundaries of a rectangle and is calculated by the formula: P = 2(l + b) units.
What is the formula for the diagonal of a rectangle?
Diagonal of a rectangle is defined as the line that joins the opposite vertices of a rectangle and is calculated using formula: (diagonal)2 = (length)2 + (breadth)2