Formula Of Perimeter Shapes

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The perimeter of a shape is the distance around all four edges of the object. A form's area is the flat space inside the shape. You will also learn how to compute the areas of parallelograms, rhombi, kites, and trapeziums, as well as study the effect of doubling the dimensions of a shape on its perimeter and area.

Read Also: Class 9 Congruence of Triangles


What is Perimeter?

A perimeter is the length of a two-dimensional shape's boundary. It is sometimes defined as the total of the lengths of all the object's sides. The perimeter of a form is the algebraic sum of the lengths of its sides. In geometry, we have formulas for the various shapes. 

The perimeter of a geometric shape is the distance between its edges. In other terms, it is the entire sum of the lengths of all the sides of two-dimensional geometry. As a result, the perimeter of every figure is the total of the lengths of each side. In this section, we will go through the perimeter formula for various geometric shapes. Let's get started!


Formula for Perimeter

A perimeter is the length of a closed geometric figure's boundary. The perimeter formula for regular polygons can be represented using algebraic equations. Assume that each side of a regular polygon is l in length. The perimeter of shapes formula can be given for each polygon using the same variable l.

Example: The formula must be used to calculate the perimeter of a rectangular box with a length of 6 cm and a width of 4 cm.

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The Perimeter of Different Shapes

Perimeter of Hexagon

A hexagon is a six-sided polygon with six edges. A hexagon has six equal sides, and each interior angle is 120 degrees.

  • Hexagon's perimeter = 6 a, where 'a' is a hexagon's side.

Hexagon

Hexagon

Perimeter of Kite 

A kite is a plane figure with two equal-sized pairs.

  • A kite's perimeter is equal to 2a + 2b, where an is the length of the first pair and b is the length of the second pair.

Kite

Kite

Check Important Notes for Remainder Theorem

Perimeter of Rhombus

A Rhombus is a plane shape with four identical sides and four angles. These angles must be at least 90 degrees. The opposite sides of the Rhombus, on the other hand, must be parallel to each other. A rhombus' form is frequently compared to that of a diamond. A square is also known as a rhombus since it meets all of the criteria for a rhombus. The altitude of a rhombus is the distance between two sides at right angles. It should also be noted that the diagonals bisect each other at 90 degrees.

  • A rhombus' perimeter equals 4, where 'a' is a rhombus side.

Rhombus

Rhombus

Perimeter of Trapezoid 

A trapezoid is a shape that is made up of polygons. It is a quadrilateral with at least two sides that are parallel to each other. A trapezium's altitude is the perpendicular distance between its parallel sides.

  • The perimeter of a trapezoid = a + b + c + d, where a, b, c, and d are the lengths of the trapezium's sides.

Trapezoid

Trapezoid

Read More: Semicircle

Perimeter of Parallelogram 

A parallelogram is a two-dimensional figure with opposite sides that are equal and parallel.

  • Parallelogram perimeter = 2(B + H), where 'B' is the base and 'H' is the height of the parallelogram.

Parallelogram

Parallelogram

Perimeter of Square 

A square is a two-dimensional figure with equal sides. So, let's have a look at the perimeter formula for a square.

  • A square's perimeter = 4a, where 'a' is the length of a square's side.

Square

Square

Read Also: Area Segment Circle

Perimeter of Triangle 

A triangle is a two-dimensional figure with three sides. An equilateral triangle has three equal sides, whereas an isosceles triangle has two equal sides. A scalene has three sides that are all different lengths.

The following conditions must be met in order for a triangle to exist:

a + b > c

b + c > a

c + a > b

  • Triangle Perimeter = a + b + c, where 'a', 'b', and 'c' are the triangle's sides.

Triangle

Triangle

Perimeter of Rectangle

A rectangle is a two-dimensional figure with equal opposed sides.

  • Rectangle perimeter = 2(l + b), where 'l' is the rectangle's length and 'b' is the rectangle's breadth.

Rectangle

Rectangle

Read More: Similarity of Triangles


Perimeter Formulas for 2D shapes

The perimeter formulas for several 2D forms are given below-

Shapes Perimeter Formula Metrics
Hexagon 6 x a a = Length of a side
Kite 2a + 2b a = Length of the first pair b = Length of the second pair
Rhombus 4 x a a = Length of a side
Trapezoid a + b + c + d a, b, c, d being the sides of the trapezoid
Parallelogram 2(Base + Height) -
Square 4a a =Length of a side
Triangle a + b + c a, b and c being the side lengths
Rectangle 2(Length + Width) -

Things to Remember-

  • Perimeter is defined as the total of the lengths of all the object's sides. The perimeter of a form is the algebraic sum of the lengths of its sides.
  • Hexagon's perimeter = 6 a, where 'a' is a hexagon's side.
  • A kite's perimeter is equal to 2a + 2b, where an is the length of the first pair and b is the length of the second pair.
  • A rhombus' perimeter equals 4, where 'a' is a rhombus side.
  • The perimeter of a trapezoid = a + b + c + d, where a, b, c, and d are the lengths of the trapezium's sides.
  • Parallelogram perimeter = 2(B + H), where 'B' is the base and 'H' is the height of the parallelogram.
  • A square's perimeter = 4a, where 'a' is the length of a square's side.
  • Triangle Perimeter = a + b + c, where 'a', 'b', and 'c' are the triangle's sides.
  • Rectangle perimeter = 2(l + b), where 'l' is the rectangle's length and 'b' is the rectangle's breadth.

Checkout Important Notes for


Sample Questions

Ques: Find the perimeter of a rectangular box, with a length of 8 cm and breadth of 2 cm.

Sol: Use the formula,

Perimeter of a Rectangle = 2 (L+B)

Given- 

L= 8 cm

B= 2 cm

Hence, 

P= 2 ( 8 cm + 2 cm) 

= 2 × 10 cm

 = 20 cm.

Ques: How to find the area and perimeter of a square? Find the perimeter of a square if the area is 16 cm2.

Sol: A square is a shape with all the four sides equal in length. These four sides are also parallel to each other. They also make an angle of 90° with each other. To find the area and perimeter of the square, we need to know the measurement of one side of the square.

Area of a square = (Side)2, and

Perimeter of a square = 4(Side)

Given: Area is 16 cm2 

(Side)2 = 16

Or Side = 4 (Ignored negative value as length cannot be negative)

Again, using the perimeter formula, we have

Perimeter = 4(Side) = 4 x 4 = 16

So, 24 cm is the perimeter of a square.

Read Also: Area of Sector

Ques. Find the perimeter of a rectangle with a length of 20 cm and breadth of 25 cm.

Sol: Using the formula,

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

Given-

L= 20 cm

B=25 cm

= 2 (20 + 25) cm

= 2 x 45 cm

= 90 cm

Ques. Find the perimeter of a triangle with sides 5 cm, 6 cm and 5 cm.

Sol: Perimeter of a Triangle = a + b + c

Where, a,b and c are sides.

Given-

a= 5 cm

b= 6 cm

c= 5 cm

Hence, 

P = 5 + 6 + 5

= 16 cm

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CBSE X Related Questions

  • 1.
    Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).


      • 2.

        In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.


          • 3.
            Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
            (i) $pqr + 1$ is a composite number
            (ii) $pqr + 1$ is a prime number


              • 4.

                From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid.
                Use $\pi = \dfrac{22}{7}, \sqrt{5} = 2.2$


                  • 5.

                    Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
                    Choose the correct option from the following:
                    (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
                    (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
                    (C) Assertion (A) is true, but Reason (R) is false.
                    (D) Assertion (A) is false, but Reason (R) is true.

                    Assertion (A): For any two prime numbers $p$ and $q$, their HCF is 1 and LCM is $p + q$.
                    Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

                      • Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
                      • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
                      • Assertion (A) is true, but Reason (R) is false.
                      • Assertion (A) is false, but Reason (R) is true.

                    • 6.
                      In a right triangle ABC, right-angled at A, if $\sin B = \dfrac{1}{4}$, then the value of $\sec B$ is

                        • 4
                        • $\dfrac{\sqrt{15}}{4}$
                        • $\sqrt{15}$
                        • $\dfrac{4}{\sqrt{15}}$

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