# Mensuration Formula

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Here’s what is mensuration in mathematics. We can define mensuration as the branch of mathematics that studies the measurement of various different 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

Now we know what is mensuration in mathematics. Mensuration can be defined as the branch of mathematics which talks about the length, volume or area of different geometric shapes. These shapes exist in 2 dimensions or 3 dimensions. Let’s learn the difference between the two.

## Difference Between 2D and 3D shapes

 2D shape 3D shape If any shape is surrounded by three or more straight lines in a plane, then it is known as a 2D shape. If any shape is surrounded by a no. of surfaces or planes then it is known to be a 3D shape. These 2D shapes have no height or depth. These 3D shapes are also known as solid shapes and unlike 2D shapes they have both height or depth. We can measure the area and perimeter of 2D shapes. We can measure their volume, CSA, LSA or TSA of 3D shapes.

### Mensuration in Maths - Important Terminologies

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

 Terms Abbreviation Unit Definition Area A m² or cm² The area is the surface which is covered by the closed shape. Perimeter P m or cm Perimeter can be defined as the measure of the continuous line along the boundary of the given figure. Volume V $m^{3}$ or $cm^{3}$ In a 3D shape, the space included is known as the Volume. Curved Surface Area CSA m² or cm² If there’s a curved surface, then the total area is called a Curved Surface area. Example: Sphere or Cylinder. Lateral Surface area LSA m² or cm² The total area of all the lateral surfaces that surrounds the figure is called the Lateral Surface area. Total Surface Area TSA m² or cm² If 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 Unit – m² or cm² The area covered by a square of side one unit is known as a Square unit. Cube Unit – $m^{3}$ or $cm^{3}$ The volume occupied by a cube of one side one unit.

### Math Formula Mensuration

Here are the important math formula mensuration.

### 1. Square

Area of Square: Formula for Area of square (A) = a2 , where  A = Area of a square, a = Side of a square

Perimeter of Square: Formula for Perimeter of a Square (P) = 4 × a , where P = Perimeter of a square , a = Side of square

### 2. Rectangle

Perimeter of the Rectangle: P= 2 × ( L+B) , where P = Perimeter of a rectangle, L = Length of a rectangle , B= Breadth of a rectangle

Area of the Rectangle: A= L× B , where A = Area of a rectangle, L = Length of a rectangle , B= Breadth of a rectangle

### 3. Cube

Surface area of a cube: S = 6 × A2 , where S= Area of a rectangle, A= Length of the side of the cube

Volume of a cube: V =A3 where, V = Volume of the cube, A = Side of the cube

### 4. Cuboid

Surface Area of a Cuboid: S = 2 × (LB + BH + HL) ,where S = Surface Area of a cuboid, L = Length of cuboid, B= Breadth of the cuboid , H = Height of the cuboid

Volume of Cuboid: V = L × B × H, where V = Volume of the cuboid, L= Length of the cuboid, H equals to the height of the cuboid and B = Breadth of the cuboid .

### 5. Cylinder

Surface Area of a Cylinder: S= 2 × π × R × (R+H), where S= Surface Area of the Cylinder, R = Radius of the Cylinder, H =Height of the cylinder

Volume of a Cylinder: V= π × R2 × H, where V = Volume of the Cylinder, R = Radius of the Cylinder, H =Height of the cylinder

### 6. Sphere

Surface Area of a Sphere: S =4 × π × R2 , where S= Surface Area of the sphere, R = Radius of the Sphere

Volume of a Sphere: V = 4/3 × π × R3, where V= Volume of the sphere, R = Radius of the Sphere

### 7. Cone

Surface Area of a Right circular cone: S = π × r(l+r) , where S= Surface Area of the Right Circular Cone, l = Length of the cone, r = Radius of the cone

Volume of a Right circular cone: V = ( π × R2 × H ) ÷ 3, where V = Volume of the Right circular cone , H = Height of the cone.

### Questions To Be Solved

Question 1) What is the area and perimeter of a square with a side of 4 cm?

Solution)We know the formula to find the area of a square and perimeter of a square,

Area of square (A) = a2 , Here the value of a = 4 cm

Therefore, the Area of a square = 42 = 16 cm

Perimeter of square = 4 × a , We know that the value of a = 4 cm

Therefore, the Perimeter of a square = 4 × 4 = 16 cm

Question 1) How do you calculate Mensuration ? What is Mensuration?

1. Area of rectangle (A) is equal to length(l) × Breath(b)

2. Perimeter of a rectangle (P) is equal to 2 × (Length(l) + Breath(b))

3. Area of a square (A) is equal to Length (l) × Length (l)

4. Perimeter of a square (P) is equal to 4 × Length (l)

5. Area of a parallelogram (A) is equal to Length(l) × Height(h)

6. Perimeter of a parallelogram (P) is equal to 2 × (length(l) + Breadth(b))

Now we know what is mensuration in mathematics. Here’s the definition of mensuration and we can define mensuration as the branch of mathematics which deals with the study of different geometrical shapes,their areas, and Volume. In simple words, it is all about the process of measurement.

Question 2) How many types of Mensuration are there? Which topics come under Mensuration? What is the volume in Mensuration?

• Cylinder.

• Circles.

• Polygons.

• Rectangles and Squares.

• Trapezium, Parallelogram and Rhombus.

• Area and Perimeter.

• Cube and Cuboid

So let us study the topics that come under mensuration:

• Cylinder.

• Circles.

• Polygons.

• Rectangles and Squares.

• Trapezium, Parallelogram and Rhombus.

• Area and Perimeter.

• Cube and Cuboid.

Here are the Volume Formulas : We know that solid occupies some regions in space and the magnitude of this region is known as the Volume of the solid. One of the standard units of volume is cubic centimeter (cm3) .