Mensuration formulas class 10

Mensuration is a branch of mathematics that examines how to measure geometric figures and their properties, such as length, volume, shape, surface area, lateral surface area, and so on.The ancient Egyptians were the first to employ mathematical methods for land surveying and levelling. The mensuration formulas are the mathematical procedures utilised here. The height, width, depth, perimeter, area, and volume of a single object or group of objects are all provided through measurements. Mensuration describes a variety of geometrical shapes, such as two-dimensional shapes, as well as their attributes and formulas.

What is the formula of mensuration?

Mensuration is a subject of mathematics that deals with the length, volume, and area of various geometric shapes. These shapes can be found in 2-D or 3-D. It entails calculating the areas, volumes, and other properties of forms. Geometry covers many mensuration formulas and concepts that help answer the questions from everyday life.

2-D and 3-D shapes

2D Shapes- A two-dimensional shape is a flat planar figure or a shape with only two dimensions, such as length and width, in geometry. 2D forms can only have their area and perimeter calculated.

3D Shapes- A three-dimensional shape has three dimensions: length, width, and thickness. Volume, curved surface area, and total surface area of 3D forms are all calculated.

Terminology  and formula in Mensuration

·       Perimeter(P)- Unit- cm or m- A Perimeter is the length of a continuous line that runs along the boundaries of a specified figure.

·Area(A)- Unit- m2 or cm2 – The surface that is covered by the closed shape is referred to as the area.

·Volume(V)- Unit- cm3 or m3 -A volume is the amount of space occupied by a 3D form.

·Curved Surface Area (CSA)- Unit – m2 or cm2 – The overall area of a curved surface is known as the Curved Surface area. Example: Sphere

·Lateral Surface area (LSA) – Unit- m2 or cm2 – The Lateral Surface Area is the total area of all the lateral surfaces that surround the specified figure.

·Total Surface area (TSA)- Unit- m2 or cm2 -The Total Surface Area is the total of all curved and lateral surface areas.

·Square Unit- Unit- m2 or cm2 -A square unit is an area covered by a square with a side length of one unit.

·Cube Unit- Unit- cm3 or m3 -A cube of one side occupies one unit of volume.

Mensuration Formulas

Let’s go through all of the main mensuration formulas for 2D and 3D shapes now. It will be simple to solve mensuration difficulties with this collection of mensuration formulas.

Mensuration Formulas For 2D Shapes

• Square            

Area – a2

Perimeter – 4a

• Rectangle              

Area – l × b

Perimeter – 2 ( l + b)

• Circle       

Area – πr2

Perimeter – 2 π r

• Scalene Triangle                           

Area – √[s(s−a)(s−b)(s−c)],

Where, s = (a + b + c)/2

Perimeter – a + b + c

• Isosceles Triangle                          

Area – ½ × b × h

Perimeter – 2a + b

• Equilateral triangle                           

Area – (√3/4) × a2

Perimeter – 3a

• Right Angle Triangle                          

Area – ½ × b × h

Perimeter – b + h + p

• Rhombus                                        

Area – ½ × d1 × d2

Perimeter – 4 × side

• Parallelogram                              

Area – b × h

Perimeter – 2( l + b )

• Trapezium  

Area – ½ h( a + c )

Perimeter – a + b + c + d 

Mensuration Formulas for 3D Shapes             

• Cube                              

Volume- a3

Lateral Surface Area (LSA)- 4 a2

Total Surface Area (TSA) – 6 a2

• Cuboid                                    

Volume- l × b × h

Lateral Surface Area (LSA)- 2h(l + b)

Total Surface Area (TSA) – 2 (lb +bh +hl)

• Sphere                                   

Volume- (4/3) π r3

Curved Surface Area (CSA) or Lateral Surface Area (LSA)- 4 π r2

Total Surface Area (TSA) – 4 π r2

• Hemisphere                 

Volume- (⅔) π r3

Curved Surface Area (CSA) or Lateral Surface Area (LSA)- 2 π r2

Total Surface Area (TSA) – 3 π r2

• Cylinder                             

Volume- π r2 h

Curved Surface Area (CSA) or Lateral Surface Area (LSA)- 2π r h

Total Surface Area (TSA) – 2πrh + 2πr2

• Cone                                  

Volume- (⅓) π r2 h

Curved Surface Area (CSA) or Lateral Surface Area (LSA)- π r l

Total Surface Area (TSA) – πr (r + l)

Conclusion

Mensuration is a discipline of geometry concerned with the measurement of area, length, and volume in two-dimensional and three-dimensional forms. 2D objects, such as squares, rectangles, triangles, and circles, can be drawn in a plane, however 3D shapes, such as bricks, ice cream cones, and footballs, cannot. Mensuration entails the use of mathematical formulas and algebraic equations to do calculations.