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 formulas pdf in hindi

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 formulas pdf in hindi

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.

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We have attached the link of mensuration formulas pdf in hindi 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 m2 or cm2 Square Unit – m2 or cm2 Cube Unit – m3 or cm3

1. Square

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

Perimeter of the Rectangle:

B

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)

3. Circle

Area= πr2

Parameter= 2 π r

mensuration formulas pdf in hindi

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

वक्रप़ष्ठ = 6भुजा² (बाहरी भाग)

Length of the side of a cube

LSA = 4 a2

आयतन = भुजा³ (आंतरिक भाग)

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.

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5. Cuboid

वक्रप़ष्ठ = 2(lb+bh+hl) (बाहरी भाग)

LSA = 2h(l + b)

mensuration formulas pdf in hindi

आयतन = लंबाई x चौडाई x उंचाई

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

संपूर्ण प़ष्ठ = 2 × π × R × (R+H)

Height of Cylinder

आयतन = π × R2 × H (आंतरिक भाग)

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

S =4 × π × R2

R

वक्रप़ष्ठ = 3πr² (बाहरी भाग)

आयतन = (4/3) πr³ (आंतरिक भाग)

R

8. Cone

क्षेत्रफल = πr(r+s)

Slant Height of Cone

LSA = π r l

आयतन =(1/3)πr²h

Height of Cone

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9. Triangle

a+b+c

क्षेत्रफल = √ [s(s-a)(s-b)(s-c)]

2a + b

क्षेत्रफल = 1/2 x आधार x उंचाई

mensuration formulas pdf in hindi

3a

क्षेत्रफल = (√ 3)/4 x भुजा²

b + hypotenuse + h

Area (Square units): ½ × b × h

10. Rhombus

4 × side

क्षेत्रफल = 1/2 ( विकर्ण1 x विकर्ण2)

समचतुर्भुज – सभी भुजाएं बराबर और एक दुसरे के समांतर

11. Parallelogram

2(l+b)

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

12. Trapezium

a+b+c+d

समांतर समचतुर्भुज – कोई भी दो भुजा बराबर

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 = a2 square units

Substitute the value ofs “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.

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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