Important Formula: Volume, Surface Area & Solid Figures | Quantitative Aptitude for SSC CGL PDF Download

Perimeter, Area and Volume formulas for various shapes

• Geometry, a branch of mathematics, focuses on diverse shapes and sizes. It can be categorized into two types: Plane Geometry and Solid Geometry.
• Plane Geometry involves shapes like circles, triangles, rectangles, and squares.
• Solid Geometry is dedicated to calculating the length, perimeter, area, and volume of various geometric figures and shapes. Presented below are some fundamental formulas used to compute the length, area, volume, and perimeter of diverse shapes and figures.

Formulas For Perimeter Area Volume

Formulas for Square

• Here, s = side
• Perimeter: 4 * s
• Area: S2
• Diagonal: s√2
• Area of square when diagonal is given
  

Formulas for Rectangle

• Here , l = length, b = breadth.
• Perimeter: 2 (l + b) (l = length, b = breadth)
• Area: l × b
• Diameter:
• Area of 4 walls of a room = 2 (Length + Breadth) × Height
  

Formulas of Circle

• Area of circle = πr²
• Area of semi-circle= πr²/2
• Circumference of a circle = 2πr
• Circumference of a semi-circle = πr
• Length of arc
• Area of sector = 1/2 (arc*R) = πr²ɵ/360
  

Parallelogram formulas

• Perimeter: 2(a + b)
• Area: b × h
• Height of parallelogram = A/b
  

Rhombus formulas

• Perimeter: 4 × a
• Area:
• Diagonals
  
  

Trapezium formulas

• Perimeter: a + b + c + d
• Area: 1/2  × (sum of parallel sides) × distance between them
• To find thee distance between parallel sides you will have to convert trapezium to rectangle and then use Pythagoras Theorem.
  

Cube formulas

• Volume: (side)³
• Surface area = 6s²
• Partial Surface area = 4s²
• Diagonal = √3s
  

Cuboid formulas

• Volume: l * b * h
• Surface area = 2 (lb + bh + hl)
• Curved Surface area = 2h(l+b)
• Diagonal =

Sphere formulas

Formulas for Sphere

• Volume:
• Surface area = 4πr²

Hemisphere formulas

• Volume:
• Curved Surface area = 2πr²
• Total Surface area = 3πr²
  

Cylinder formulas

• Volume: πr²h
• Curved Surface area = 2πrh
• Total Surface area = 2πr (h + r)
  

Cone formulas

• Volume:
• Slant height
• Curved Surface area = πrl
• Total Surface area = πrl +πr
  

Some Examples Based On Above Formulas

Q1: Rohan Bought a House, which had a garden outside it, with sides measuring 12 meters and 8 meters, Find the perimeter of the  garden ? 
Ans: The formula to find Perimeter is , P= 2(L+W)
= 2(12+8)
=2(20)
=40m Ans.

Q2: Two kids planned to make an equilateral traingle  of a cardboard , The length of one side of  the traingle being  8 centimeters. Calculate the perimeter of the triangle.
Ans: Perimeter  of Equilateral Traingle = 3 x Side length
= 3 x 8
= 24m Ans

Q3: The base of a triangle measures 12 centimeters, and its height is 8 centimeters. Find the area of the triangle.
Ans: Area of the triangle = (Base × Height) / 2
= (12 centimeters × 8 centimeters) / 2
= 48 square centimeters.

Q4: To protect his house from Robbers, Mohan wrapped a wire around his square plot. If the wire’s length is 80 meters, what is the perimeter of the square?
Ans: Perimeter of Square Plot = 4a(Where a = length of side)
= 4 x 80
= 320m Ans.

Q5: Rahul Came up with an idea to make figure made up of two adjacent rectangles, one measuring 8 meters by 5 meters and the other 6 meters by 4 meters. Find the total area of the figure.
Ans: Total area of the figure = Area of the first rectangle + Area of the second rectangle
= (8 meters × 5 meters) + (6 meters × 4 meters)
= 40 square meters + 24 square meters
= 64 square meters.