16. Mensuration

Mensuration is the branch of mathematics which studies the measurement of the geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc. Here, the concepts of mensuration are explained and all the important mensuration formulas and properties of different geometric shapes and figures are covered.

Mensuration Maths- Definition

A branch of mathematics which talks about the length, volume or area of different geometric shapes is called Mensuration. These shapes exist in 2 dimension or 3 dimensions. Let’s learn the difference between the two.

Difference Between 2D and 3D shapes

2D Shape3D 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 as solid shapes and unlike 2D they have both height or depth.
These shapes have only 2-D length and breadth.These are called Three dimensional as they have depth, breadth and length.
We can measure their area and Perimeter.We can measure their volume, CSA, LSA or TSA.

Mensuration in Maths- Important Terminologies

Let’s learn a few more definitions related to this topic.

TermsAbbreviationUnitDefinition
AreaAM2 or Cm2The area is the surface which is covered by the closed shape.
PerimeterPCm or mThe measure of the continuous line along the boundary of the given figure is called a Perimeter.
VolumeVCm3 or m3In a 3D shape, the space included is called a Volume.
Curved Surface AreaCSAM2 or cm2If there’s a curved surface, then the total area is called a Curved Surface area. Example: Sphere or Cylinder.
Lateral Surface areaLSAM2 or cm2The total area of all the lateral surfaces that surrounds the figure is called the Lateral Surface area.
Total Surface AreaTSAMor Cm2If there are many surfaces like in 3D figures, then the sum of the area of all these surfaces in a closed shape is called Total Surface area.
Square UnitMor cm2The area covered by a square of side one unit is called a Square unit.
Cube UnitMor cm3The volume occupied by a cube of one side one unit

Mensuration Formulas

Now let’s learn all the important mensuration formulas involving 2D and 3D shapes. Using this mensuration formula list, it will be easy to solve the mensuration problems. Students can also download the mensuration formulas list PDF from the link given above. In general, the most common formulas in mensuration involve surface area and volumes of 2D and 3D figures.

Mensuration Formulas For 2D Shapes

ShapeArea (Square units)Perimeter (units)Figure
Squarea24aMensuration Formula for Square
Rectanglel × b2 ( l + b)Mensuration Formula for Rectangle
Circle?r22 ? rMensuration Formula for Circle
Scalene Triangle?[s(s?a)(s?b)(s?c)],Where, s = (a+b+c)/2a+b+cMensuration Formula for Scalene Triangle
Isosceles Triangle½ × b × h2a + bMensuration Formula for Isosceles Triangle
Equilateral Triangle(?3/4) × a23aMensuration Formula for Equilateral Triangle
Right Angle Triangle½ × b × hb + hypotenuse + hMensuration Formula for Right Angle Triangle
Rhombus½ × d1 × d24 × sideMensuration Formula for Rhombus
Parallelogramb × h2(l+b)Mensuration Formula for Parallelogram
Trapezium½ h(a+b)a+b+c+dMensuration Formula for Trapezium

Mensuration Formulas for 3D Shapes

ShapeVolume (Cubic units)Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units)Total Surface Area (TSA) (Square units)Figure
Cubea36 a2Mensuration Formula for Cube
Cuboidl × w × h2 (lb +bh +hl)Mensuration Formula for Cuboid
Sphere(4/3) ? r34 ? r24 ? r2Mensuration Formula for Sphere
Hemisphere(?) ? r32 ? r 23 ? r 2Mensuration Formula for Hemisphere
Cylinder? r 2 h2? r h2?rh + 2?r2Mensuration Formula for Cylinder
Cone(?) ? r2 h? r l?r (r + l)Mensuration Formula for Cone

Mensuration Problems

Question: Find the area and perimeter of a square whose side is 5 cm?

Solution:

Given:

Side = 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.

Register at BYJU’S to learn more on other mathematical concepts and also learn mensuration problems and formulas by downloading BYJU’S – The Learning App.

Frequently Asked Questions

What is mensuration in Maths?

In maths, mensuration is defined as the study of the measurement of various 2D and 3D geometric shapes involving their surface areas, volumes, etc.

What is the difference between mensuration and geometry?

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.

What are 2D and 3D Mensuration?

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 cube, sphere, cuboid, cone, cylinder, etc.

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