Important Mensuration Concepts and Formulas for SSC, Bank and Railways | Mensuration Concepts and Formulas

In all competitive exams, the Mensuration portion has a very good weightage, many questions are asked from this topic. So, it is very important to make this portion very strong for all competitive exams. SSC, Bank, and Railways exams have lots of questions related to Mensuration. We can't leave this topic untouched because a lot of questions come from this topic.

Mensuration is a division of mathematics that deals with geometric figures like cones, cubes, spheres, etc. We are generally asked about the volume, area, length of these figures, and shapes. Mensuration is nothing but the measurement of parameters of 2D and 3D figures.

Lateral surface area is the area of all the surfaces excluding the area of base and top. Lateral surface area is also called the curved surface area in the case of cone or sphere. Total surface area refers to the sum of lateral surface area and the area of top and bottom. 

In this article, we are providing you with the formulas of the most commonly used shapes and figures.

Mensuration Formulas for 2-D Figures:

1. Rectangle:
Area=length×width
Perimeter =2(l+w)

2. Square:
Area=side×side
Perimeter=4×side

3. Circle:
Area=Πr²
Circumference=2Πr
Diameter=2r

4. Triangle:
Area =1/2×base×height
Perimeter=a+b+c

5. Isosceles Triangle:
Area =1/2×basexheight
Perimeter=2×(a+b)

6. Scalene Triangle:
Area = 1/2×base×height
Perimeter =a+b+c

7. Right Angled Triangle:
Area =1/2×base×height
Perimeter =b+h+hypotenuse
Hypotenuse c=a²+b²

8. Parallelogram:
Area = a×b
Perimeter = 2(l+b)

9. Rhombus:
Area = 1/2×d1×d2
Perimeter = 4×side

10. Trapezium:
Area = 1/2×h(a+b)
Perimeter = a+b+c+d

11. Equilateral Triangle:
Area =√3/4×a²
Perimeter=3a

Mensuration Formulas of 3-D Figures:

1. Cube:
Lateral Surface Area =4a²
Total Surface Area =6a²
Volume =a³

2. Cuboid:
Lateral Surface Area =2h(l+b)
Total Surface Area = 2(lb+bh+lh)
Volume = length×breadth×height

3. Cylinder:
Lateral Surface Area =2Πrh
Total Surface Area =2Πrh+2Πr²
Volume = Πr²h

4. Cone:
Lateral Surface Area =Πrl
Total Surface Area =Πr(r+l)
Volume =1/3Πr²h

5. Sphere:
Lateral Surface Area =4Πr²
Total Surface Area =4Πr²
Volume =(4/3)Πr³

6. Hemisphere:
Lateral Surface Area =2Πr²
Total Surface Area =3Πr²
Volume =(2/3)Πr³