Basic Geometry Formulas

Last Updated : 22 Apr, 2026

In mathematics, geometry stands as a discipline of study and is a subject for the analysis of shapes and structures along with their properties.

Geometrical formulas are the standard derived formulas for the calculation of parameters of shapes. These parameters are area, volume, perimeter, circumference, total surface area, lateral surface area, etc.These formulas are listed below.

2D Geometry Formulas

The geometry formulas for 2D shapes are tabulated below:

2D Shape

Formulas

Triangle

  • Perimeter = Sum of three Sides
  • Area = 1/2 × base × height

Rectangle

  • Perimeter = 2(length + breadth)
  • Area = length × breadth
  • Diagonal = \sqrt {(length^2 + breadth^2)}

Square

  • Perimeter = 4 × Side
  • Area = Side × Side
  • Diagonal = \sqrt {2} × Side

Parallelogram

  • Perimeter = 2(length + breadth)
  • Area = base × height

Rhombus

  • Perimeter = 4 × Side
  • Area = 1/2(diagonal1 × diagonal2)

Trapezium

  • Perimeter = Sum of all sides
  • Area = 1/2 × height × (Sum of Parallel Sides)

Circle

  • Perimeter = 2Ï€r
  • Area = Ï€r2

3D Geometry Formulas

The geometry Formulas for 3D figures are mentioned below:

3D Shape

Formulas

Cube

  • Surface Area of Cube = 6a2
  • LSA of Cube = 4a2
  • Volume of Cube = a3

Cuboid

  • Surface Area of Cuboid = 2(lb + bh + hl)
  • LSA of Cuboid = 2(l + b)h
  • Volume of Cuboid = l × b × h

Cylinder

  • Curved Surface Area of Cylinder = 2Ï€rh
  • Total Surface Area of Cylinder = 2Ï€r(r + h)
  • Volume of Cylinder = V = Ï€r2h

Cone

  • Curved Surface Area of a Cone = Ï€rl
  • Total Surface Area of Cone = Ï€r(r + l) = Ï€r[r + \sqrt{(h^2 + r^2)}]
  • Volume of a Cone = V =1/3 × Ï€r2h

Sphere

  • Surface Area of a Sphere = 4Ï€r2
  • Volume of a Sphere = 4/3 × Ï€r3

Hemisphere

  • Curved Surface Area of a hemisphere = 2Ï€r2
  • Surface Area of a hemisphere = 3Ï€r2
  • Volume of a hemisphere = 2/3 × Ï€r3

Also Check:

Solved Examples

Problem 1. If the radius of a circle is 14cm. Find the area of the given circle.

Solution:

Given

Radius of the circle is 14cm.

We have,

Area of the circle (A)=Ï€r2

=>22/7 × 14 × 14

=>616cm2

Problem 2. Find the area of a triangle with a base of 12cm and a height of 8cm.

Solution:

Given

Base of the triangle is 12cm.

Height of the triangle is 8cm.

We have,

Area of triangle(A)=1/2 × b × h

=>1/2 × 12 × 8

=>48cm2

Problem 3. Find the perimeter of the given rectangle with a length of 10cm and breadth of 4cm.

Solution:

Given

Length of the rectangle is 10cm.

Breadth of the rectangle is 4cm.

We have,

Perimeter of rectangle(P)= 2(l+b)

=>2(10+4)

=>2 × 14

=>28cm

Problem 4. Find the perimeter of a square having a length of 5cm.

Solution:

Given

Length of the square is 5cm.

We have,

Perimeter of the square(P)= 4l

=> 4 × 5

=>20cm

Problem 5. Find the volume of a sphere having a radius of 9cm.

Solution:

Given

Radius of the sphere is 9cm.

We have

Volume of a sphere(V)=4/3 πr3

=>4/3 × 22/7 × (9)3

=>3054.85cm3

Problem 6. Calculate the area of a trapezoid having bases 8cm and 10cm and height of 12cm.

Solution:

Given

Let the bases of the trapezoid be b1 and b2 with values 8cm and 10cm respectively.

Height of the trapezoid is 12cm.

We have,

Area of Trapezoid = A =1/2 × (b1 + b2) × h

=>1/2 × (8 +10) × 12

=>1/2 × 18 × 12

=>216/2

=>108cm2

Problem 7. Find the volume of the given cone having a radius of 6cm and a height of 12cm.

Solution:

Given

Radius of the cone is 6cm.

Height of the given cone is 12cm

We have,

Volume of a Cone = V = 1/3× πr2h

=>1/2 × 22/7 × (6)2 × 12

=>9504/14

=>678.85cm3

Problem 8. Calculate the curved surface area of a cylinder having a radius of 4cm and a height of 8cm.

Solution:

Given

Radius of the cylinder is 4cm.

Height of the cylinder is 8cm.

We have,

Curved surface area= 2Ï€rh

=>2 × 22/7 × 4 × 8

=>201.14cm2

Problem 9. Calculate the area of a cube box having a side of 3cm.

Solution:

Given

Length of a side is 3cm.

We have,

Area of cube(A)= 6a2

=> 6 × 3 ×3

=>54cm2

Practice Problems

Problem 1: Calculate the area and perimeter of a rectangle having the length 5 cm and width 3 cm.

Problem 2: Find out the area and circumference of a circle having the radius 4cm (Use π ≈ 3.14 approximately).

Problem 3: Calculate the area and perimeter of a square using the side length 6 cm.

Problem 4: Find the surface area of a rectangular prism using the length 6 cm, 4 cm and height 5 cm.

Problem 5: Find out the area of an equilateral triangle using the 8 cm side length.

Problem 6: Calculate the volume and surface area of a cube having the edge length is 10 cm.

Problem 7: Find the volume and surface area of a sphere using the radius 6 cm (Use π≈3.14).

Problem 8: Find out the distance between points having the A(2,3) and B(5,7).

Problem 9: Find the midpoint of the line segment joining points using the C (−1,2) and D (3,6).

Problem 10: calculate the area having a trapezoid with bases values such as b1 is 8 cm, b2 is 5 cm, and height is 4 cm.

Key Answer:

  1. Area: 15 cm², Perimeter: 16 cm
  2. Area: 50.24 cm², Circumference: 25.12 cm
  3. Area: 36 cm², Perimeter: 24 cm
  4. Surface Area = 148 cm²
  5. Area: ≈27.71 cm²
  6. Volume: 1000 cm³, Surface Area: 600 cm²
  7. Volume: ≈904.32 cm³, Surface Area: ≈452.16 cm²
  8. Distance: ≈3.61 units
  9. Midpoint: (1, 4)
  10. Area: 26 cm²
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