Detailed mensuration formula pdf in hindi download

Mensuration formula pdf are extensively used to solve problems related to finding areas and volumes of two dimensional (2D) geometry and three dimensional (3D) geometry figures, measurement of the geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc & measurement of the geometrical figures and shapes like cube, cuboid, cone, sphere, cylinder, etc. We have compiled the most frequently used mensuration formulas in competitive exams like CAT and SSC SGC. However, this list of mensuration formulas is also helpful to students who are in schools.

 

Mensuration Formula

 

What is Mensuration?

Mensuration is useful about the measurement of shapes and figures. It is applicable with 2-D and 3-D geometrical shapes both. Using a specific mensuration formula from the many, we will able to solve the mensuration problems easily. So let us see these concepts of mensuration and their formulas.

If a shape is surrounded by three or more straight lines in a plane surface, then it is a 2-D shape. And such shapes are having only length and breadth. If a shape is surrounded by a no. of surfaces or planes then it is termed as 3-D shape. These are having depth, breadth, and length.

mensuration formula pdf

 

Differences Between 2D and 3D shapes

 

2D Shape

3D Shape

If a shape is surrounded by three or more straight lines in a plane, then it is a 2D shape.

If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape.

These shapes have no depth or height.

These are also called solid shapes and unlike 2D they have height or depth.

These shapes have only two dimensions say length and breadth.

These are called Three dimensional as they have depth (or height), breadth and length.

We can measure their area and Perimeter.

We can measure their volume, CSA, LSA or TSA.

 

Download Mensuration Formula PDF in English & Hindi

 

We share also Math Trick Notes PDF DownloadMath Tricks in Hindi for all Competitive Exams. You can easily save Important Questions For SSC CGL with Solution in Hindi PDF Download.

 

We have attached the link of Mensuration Formulas PDF Download below. With the help of which you can download the notes of the Mensuration Formula given by us in PDF. The PDF link that we have placed. Many Formulas related to Mensuration have been sung in it. You can prove to be very important for any Exams.

 

Mensuration in Maths- detailed definition

Terms

Abbreviation

Unit

Area

A

m2 or cm2

Perimeter

P

cm or m

Volume

V

cm3 or m3

Curved Surface Area

CSA

m2 or cm2

Lateral Surface area

LSA

m2 or cm2

Total Surface Area

TSA

mor cm2

Square Unit

mor cm2

Cube Unit

mor cm3

 

 

1. Square

Square mensuration formula
 

 

Area of Square:

A = a2

क्षेत्रफल = भुजा²

 

A

Area

a

side

 

 

Perimeter of Square:

P = 4 × a

परिमाप = 4 x भुजा

 

P

Perimeter

a

side

 

 

Extra Details:-

  1. वर्ग (Square) की सभी भुजाएं आपस में बराबर होती है और प्रत्येक कोण समकोण (90°) होता है.

  2. वर्ग के विकर्ण बराबर होते हैं और एक दूसरे को 90° अंश पर समद्वीभाजित करते हैं।

  3. विकर्ण = भुजा√ 2

 

वर्ग से सम्बंधित शॉर्ट ट्रिक्स (Square Formulas PDF Download)

 

2. Rectangle

Rectangle mensuration formula

 

Perimeter of the Rectangle:

P= 2 × ( L+B)

परिमाप = 2(लंबाई + चौडाई)

 

P

Perimeter

L

Length

B

Breadth

        Area of the rectangle:

        A= L× B

        क्षेत्रफल = लंबाई x चौडाई

         

        A

        Area

        L

        Length

        B

        Breadth

              Extra details:-

                1. आयत (Rectangle) चार भुजाओं से गिरी हुई एक आकृति है

                2. आयत का प्रत्येक कोण 90 अंश का होता है और आमने सामने की भुजा समांतर और बराबर होती हैं

                3. आयत के विकर्ण बराबर होते हैं तथा एक दूसरे को समद्वीभाजित करते हैं।

                4. विकर्ण = √ (लंबाई² +चौडाई²)

               

              आयत से सम्बंधित सभी सूत्र ( Rectangle Formulas PDF Download )

               

               

                3. Circle  

                Circle mensuration formula

                 

                Area of the Circle:

                Area= πr2

                 

                Parameter of the Circle:

                Parameter= 2 π r

                 

                mensuration formula pdf

                 

                वृत्त से सम्बंधित सभी सूत्र एवं शॉर्ट ट्रिक्स ( Circle Formulas PDF Download )

                 

                No.-1. वृत्त (Circle) एक ऐसा बिंदुपथ है जिसकी दूरी एक नियत बिंदु से हमेशा समान होती है।

                No.-2. यह नियत बिंदु वृत्त का केंद्र(Centre) कहलाता है और केंद्र से इसकी दूरी त्रिज्या (Radius) कहलाती है।

                No.-3. वृत्त को घेरने वाली रेखा को वृत्त का परिधि (Circumference) कहते हैं।

                No.-4. वृत्त के अंदर एक ऐसी रेखा जो केंद्र से होकर गुजरती है तथा दोनों तरफ परिधि से मिलती है उसे वृत्त का व्यास (Diameter) कहते हैं।

                No.-5. वृत्त के अंदर एक ऐसी रेखा जो दोनों तरफ परिधि से मिलती है परंतु केंद्र से होकर नहीं गुजरती है उसे वृत्त का जीवा (Chord) कहते हैं।

                No.-6. वृत्त की परिधि पर स्थित दो बिंदुओं की लंबाई (वक्र में) वृत्त चाप (Arc) कहलाता है यह वृत्त की परिधि का एक भाग होता है।

                1. क्षेत्रफल = πr² (आंतरिक भाग)

                2. परिधी = 2πr (बाहरी भाग)

                3. Area of a square inscribed in a circle of radius r is 2r2.

                4. Side of a square inscribed in a circle of radius r is √2 r.

                 

                वृत्त से सम्बंधित सभी सूत्र एवं शॉर्ट ट्रिक्स (Circle Formulas PDF Download)

                 

                 

                4. Cube

                Cube mensuration formula

                 

                Surface area of a cube:

                S = 6 × A2

                वक्रप़ष्ठ = 6भुजा² (बाहरी भाग)

                 

                S

                The surface area of a cube

                A

                Length of the side of a cube

                 

                Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units):

                LSA = 4 a2

                 

                Volume (Cubic units): A3

                आयतन = भुजा³ (आंतरिक भाग)

                 

                V

                Volume of cube

                A

                side of cube

                 

                Extra Details:-

                घन (Cube) एक ठोस आकृति होती है जिसमें लंबाई, चौड़ाई तथा ऊंचाई तीनों बराबर रहती हैं।

                1. विकर्ण = भुजा√ 3

                2. The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is 6 : π.

                 

                Download NCERT Mensuration Book PDF

                 

                5. Cuboid

                Cuboid mensuration formula

                 

                Surface Area of a Cuboid:

                S =2 × (LB + BH + HL)

                वक्रप़ष्ठ = 2(lb+bh+hl) (बाहरी भाग)

                 

                S

                Surface Area of Cuboid

                L

                Length of Cuboid

                B

                Breadth of Cuboid

                H

                Height of Cuboid

                  Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units):

                  LSA = 2h(l + b)

                   

                  mensuration formula pdf

                   

                  Volume (Cubic units): l × b × h

                  आयतन = लंबाई x चौडाई x उंचाई

                   

                  V

                  Volume of Cuboid

                  L

                  Length of Cuboid

                  B

                  Breadth of Cuboid

                  H

                  Height of Cuboid

                   

                  Extra Details:-

                  घनाभ (Cuboid) में चार फलक होते हैं इसकी सभी भुजाएं/ किनारों/ फलको का मिलान समकोण पर अर्थात 90° पर होता है सम्मुख फलकों के युग्म  समान होते हैं।

                  1. विकर्ण = √ (लंबाई² + चौडाई² + उंचाई²)

                   

                  घन और घनाभ से सम्बंधित सभी सूत्र (Cube and cuboid Formulas PDF Download)

                   

                  6. Cylinder

                  Cylinder mensuration formula

                   

                  Surface Area of a Cylinder:

                  S= 2 × π × R × (R+H)

                  संपूर्ण प़ष्ठ = 2 × π × R × (R+H)

                   

                  S

                  Surface Area of Cylinder

                  R

                  The radius of Circular Base

                  H

                  Height of Cylinder

                   

                  Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units):

                  LSA = 2π r h

                  वक्रप़ष्ठ = 2πrh (बाहरी भाग)

                  Volume (Cubic units): π × R2 × H

                  आयतन = π × R2 × H (आंतरिक भाग)

                   

                  V

                  Volume of Cylinder

                  R

                  The radius of Circular Base

                  H

                  Height of Cylinder

                   

                  Extra Details:-

                  एक आयत को उसकी एक भुजा के परित चारों तरफ घुमाने पर प्राप्त त्रिविमीय आकृति बेलन (Cylinder) होता है।

                   

                  बेलन तथा शंकु से सम्बंधित सभी सूत्र (Cylinder and Cone Formulas PDF Download)

                   

                  7. Sphere

                  Sphere mensuration formula

                   

                  Surface Area of a Sphere:

                  S =4 × π × R2

                   

                  S

                  Surface Area of Sphere

                  R

                  Radius of Sphere

                   

                   

                  Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units):

                  LSA = 3 π r2

                  वक्रप़ष्ठ = 3πr² (बाहरी भाग)

                   

                  Volume (Cubic units): (4/3) π r3

                  आयतन = (4/3) πr³ (आंतरिक भाग)

                   

                  V

                  Volume of Sphere

                  R

                  Radius of Sphere

                   

                   

                  गोले से सम्बंधित सभी सूत्र (Sphere Formulas PDF Download)

                   

                  8. Cone

                  Cone mensuration formula

                   

                  Surface Area of a Right circular cone:

                  S = π × r(l+r)

                  क्षेत्रफल = πr(r+s)

                   

                  S

                  Surface Area of Cone

                  R

                  The radius of Circular Base

                  L

                  Slant Height of Cone

                   

                   

                  Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units):

                  LSA = π r l

                   

                  Volume (Cubic units): (1/3)πr²h

                  आयतन =(1/3)πr²h

                   

                  V

                  Volume of Cone

                  R

                  The radius of Circular Base

                  H

                  Height of Cone

                   

                   

                  Download Detailed Mensuration formulas PDF

                   

                  9. Triangle

                  Scalene Triangle mensuration formula

                  9.1 Perimeter of a Scalene Triangle:

                  a+b+c

                   

                  Area (Square units): √[s(s−a)(s−b)(s−c)], Where, s = (a+b+c)/2

                  क्षेत्रफल = √ [s(s-a)(s-b)(s-c)]

                   

                   

                  Isosceles Triangle mensuration formula

                  9.2 Perimeter of a Isosceles Triangle:

                  2a + b

                   

                  Area (Square units): ½ × b × h

                  क्षेत्रफल = 1/2 x आधार x उंचाई

                   

                  mensuration formula pdf

                   

                   

                  equilateral Triangle mensuration formula

                  9.3 Perimeter of a equilateral Triangle:

                  3a

                   

                  Area (Square units): (√3/4) × a2

                  क्षेत्रफल = (√ 3)/4 x भुजा²

                   

                   

                  Right Angle Triangle mensuration formula

                  9.4 Perimeter of a Right Angle Triangle:

                  b + hypotenuse + h

                   

                  Area (Square units): ½ × b × h

                   

                  त्रिभुज से सम्बंधित सभी सूत्र (Triangle Formulas PDF Download)

                   

                  10. Rhombus

                  Rhombous mensuration formula

                   

                  Perimeter of a Rhombus:

                  4 × side

                   

                  Area (Square units): ½ × d1 × d2

                  क्षेत्रफल = 1/2 ( विकर्ण1 x विकर्ण2)

                   

                  समचतुर्भुज – सभी भुजाएं बराबर और एक दुसरे के समांतर

                   

                  mensuration formula pdf

                  11. Parallelogram

                  parallelgram mensuration formula

                   

                  Perimeter of a Parallelogram:

                  2(l+b)

                   

                  Area (Square units): b × h

                  क्षेत्रफल = आधार x उंचाई

                  समलंब समचतुर्भुज – आमने -सामने कि कोई भी दो भुजा समांतर

                   

                   

                  12. Trapezium

                  trapezium

                   

                  Perimeter of a Trapezium:

                  a+b+c+d

                   

                  Area (Square units): ½ h(a+b)

                  क्षेत्रफल = 1/2 ( समांतर भुजाओं का योग) x उंचाई

                  समांतर समचतुर्भुज – कोई भी दो भुजा बराबर

                   

                   

                  चतुर्भुज से सम्बंधित सभी सूत्र (Quadrilateral Formulas PDF Download)

                   

                  दो गोले दो बेलन तथा दो घन से सम्बंधित शॉर्टकट (Two Cube, Cuboid, Cylinder Formulas PDF Download)

                   

                  Mensuration Problems

                   

                  Q.1: Find out the height of a cylinder with a circular base of radius 70 cm and volume 154000 cubic cm.

                  Solution: A given here,

                  r= 70 cm

                  V= 154000 cubic cm

                  Since formula is,

                  V = π × R2 × H

                  i.e. h =Vπ×R²Vπ×R²

                  = 10 cm

                  Therefore, height of the cylinder will be 10 cm.

                   

                  Q.2: Find the area and perimeter of a square whose side is 5 cm.

                  Solution: A given here,

                  Side = a = 5 cm

                  Area of a square = asquare units

                  Substitute the value of “a” in the formula, we get

                  Area of a square = 52
                  A = 5 x 5 = 25

                  Therefore, the area of a square = 25 cm2

                  The perimeter of a square = 4a units

                  P = 4 x 5 =20

                  Therefore, the perimeter of a square = 20 cm.

                   

                  Frequently Asked Questions:

                   

                  Q. What is the difference between mensuration and geometry?

                  Ans. Mensuration refers to the calculation of various parameters of shapes like the perimeter, area, volume, etc. whereas, geometry deals with the study of properties and relations of points and lines of various shapes.

                  Q. What are 2D and 3D Mensuration?

                  Ans. 2D mensuration deals with the calculation of various parameters like area and perimeter of 2-dimensional shapes like square, rectangle, circle, triangles, etc.

                  3D mensuration is concerned with the study and calculation of surface area, lateral surface area, and volume of 3-dimensional figures like a cube, sphere, cuboid, cone, cylinder, etc.

                  Q. What is mensuration formula?

                  Ans. It studies the measurement of the geometrical figures and shapes like cube, cuboid, cone, sphere, cylinder, etc. … We can measure various terms like surface area, volume, perimeter, etc.

                   

                  Q. What are the types of mensuration?

                  Ans. Mensuration

                  • Circles.
                  • Polygons.
                  • Rectangles and Squares.
                  • Trapezium, Parallelogram and Rhombus.
                  • Area and Perimeter.
                  • Cube and Cuboid.

                   

                  Q. What is the use of mensuration?

                  Ans. Mensuration tells us about the lengths of sides, heights and perimeters, measures of angles, surface areas and volumes of 2-dimensional plates and 3-dimensional solids. Examples of different shapes are triangle, square, polygon, cylinder, cone, pyramid, cuboid etc. APPLICATIONS: Real life applications are many

                   

                  Q. Who invented mensuration?

                  Ans. Archimedes

                  Answer: The mensuration was discovered by Archimedes

                   

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