Mensuration Formulas for SSC and Banking
Introduction to Mensuration is important to help you clear your basics and master this important topic for IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams. We have all studied this topic in high school and know that it is a formula oriented topic. There are specific formulas for different parameters, we put the values in these Mensuration formulas and get the desired answers.
What is Mensuration?
Mensuration is a topic in Geometry which is a branch of mathematics. Mensuration deals with length, area and volume of different kinds of shape- both 2D and 3D. So moving ahead in the introduction to Mensuration, let us discuss what are 2D and 3D shapes and the difference between them.
1. Mensuration Formulas for RECTANGLE
- Area of Rectangle = Length × Breadth.
- Perimeter of a Rectangle = 2 × (Length + Breadth)
- Length of the Diagonal = √(Length2 + Breadth2)
2. Mensuration Formulas for SQUARE
- Area of a Square = Length × Length = (Length)2
- Perimeter of a square = 4 × Length
- Length of the Diagonal = √2 × Length
3. Mensuration Formulas for PARALLELOGRAM
- Area of a Parallelogram = Length × Height
- Perimeter of a Parallelogram = 2 × (Length + Breadth)
4. Mensuration Formulas for TRIANGLE
- Area of a triangle=(1/2)(Base × Height)=(1/2)(BC×AD)
For a triangle with sides measuring a, b and c, respectively:
- Perimeter = a + b + c
- s = semi perimeter = perimeter/2 = (a+b+c)/2
- Area of Triangle, A=
(This is also known as “Heron’s formula”)
- Area of isosceles triangle =
(Where a = length of two equal side, b = length of base of isosceles triangle.)
- Area of an equilateral triangle =
(Where, a is the side of an equilateral triangle)
5. Mensuration Formulas for TRAPEZIUM
- Area of a trapezium = (1/2) × (sum of parallel sides) × (distance between parallel sides)
= (1/2) × (AB+DC) × AE
- Perimeter of a Trapezium = Sum of All Sides
6. Mensuration Formulas for RHOMBUS
- Area of a rhombus=(1/2)×Product of diagonals
- Perimeter of a rhombus = 4 × l
(where l = length of a side)
7. Mensuration Formulas for CIRCLE and SEMICIRCLE
In the following formulae, r = radius and d = diameter of the circle
- Area of a circle = πr2= (πd2)/4
- Circumference of a circle = 2πr = πd
- Circumference of a semicircle = πr
- Perimeter of the semicircle = (πr+d)
- Area of semicircle =(πr2)/2
- Length of an arc = (2πrθ)/360, where θ is the central angle in degrees.
- Area of a sector = (1/2) × (length of arc) × r = (πr2θ)/360
8. Mensuration Formulas for CUBOID
In the following formulae, l = length, b = breadth and h = height
- Total surface area of cuboid = 2 (lb + bh + lh)
- Length of diagonal of cuboid= √(l2+b2+h2)
- Volume of cuboid = l × b × h
9. Mensuration Formulas for CUBE
In the following formulae, a = side of a cube
- Volume of cube = a3
- Total surface area of cube = 6a2
- Length of Leading Diagonal of Cube = a√3
10. Mensuration Formulas for CONE
In the following formulae, r = radius of base, l = slant height of cone and h = height of the cone (perpendicular to base)
- Slant height of a cone = l =√(h2+r2 )
- Curved surface area of a cone = C = π × r × l
- Total surface area of a cone = π × r × (r + l)
- Volume of right circular cone =1/3 πr2h
11. Mensuration Formulas for CYLINDER
In the following formulae, r = radius of base, h = height of cylinder
- Curved surface area of a cylinder = 2πrh
- Total surface area of a cylinder = 2πr(r + h)
- Volume of a cylinder = πr2h
12. Mensuration Formulas for SPHERE
In the following formulae, r = radius of sphere, d = diameter of sphere
- Surface area of a sphere = 4πr2 = πd2
- Volume of a sphere = (4/3) πr3 = (1/6)πd3
13. Mensuration Formulas for HEMISPHERE
In the following formulae, r = radius of sphere
- Volume of a hemisphere =(2/3)πr3
- Curved surface area of a hemisphere = 2πr2
- Total surface area of a hemisphere = 3πr2
14. Mensuration Formulas for HOLLOW CYLINDER
Hollow cylinder made by cutting a smaller cylinder of same height and orientation out of a bigger cylinder.
- Volume of hollow cylinder = πh(R2– r2)
(Where, R = radius of cylinder, r = radius of cavity, h = height of cylinder)
15. Mensuration Formulas for FRUSTUM OF A RIGHT CIRCULAR CONE
Frustum is created when a plane cuts a cone parallel to its base.
In the following formulae, R = radius of the base of the frustum, r = radius of the top of the frustum,
h = height of the frustum, l = slant height of the frustum
- If a cone is cut by a plane parallel to the base of the cone, the lower part is called the frustum of the cone.
- Slant height of the frustum =l=√(h2+(R-r)2)
- Curved surface area of frustum = π(R + r)l
- Total surface area of frustum = π(R + r)l + π(R2 + r2)
- Volume of the frustum=(1/3)πh(R2+r2+Rr)
16. Mensuration Formulas for PRISM
- Prism consists of two polygonal bases which are parallel to each other.
- These bases are joined by lateral faces, which are perpendicular to the polygonal bases.
- The number of lateral faces is equal to the number of sides in the polygonal base. Thus, the base of a prism could be of various shapes, namely, triangular, quadrangular, pentagonal etc.
- Volume of prism = Base area × height
- Lateral surface area of prism = perimeter of base × height
- Total surface area of prism = Lateral surface area + (2 × base area)
17. Mensuration Formula for PYRAMID
- Pyramid consists of a polygonal base and triangles at its sides. These triangles are called faces.
- The base could be of any shape, whereas the faces are generally isosceles triangles.
- All these triangular faces meet in a single point called the apex.
- Total surface area of pyramid = base area + (number of sides × ½ × slant height × base length)
- Volume of pyramid = (1/3) × base area × height
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