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Basic Geometry Formulas

Last Updated : 24 Jul, 2024
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In mathematics, geometry stands as a discipline of study and subject for the analysis of shapes and structures along with their properties. The article below illustrates the standard and derived formulas of geometry for the calculation of various parameters of a particular shape. These formulas are used to determine the unknown volume, area, perimeter, length of sides and diagonals, etc.

Table of Content

What are Basic Geometry Formulas?

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. Every shape studied under geometry has its distinct formula. These formulas are listed below.

Square Formulas

Various square formulas are,

Square-in-Maths

Where ‘a’ is the length of the sides of a square

Rectangle Formulas

Various rectangle formulas are,

Rectangle-ABCD

Where ‘l’ is Length and ‘b’ is Breadth

Triangle Formulas

Various triangle formulas are,

triangle-parts

Where,

  • ‘b’ is the base of the triangle 
  • ‘h’ is the height of the triangle

Trapezoid Formulas

Trapezium-(1)

Where,

  • b1 and b2 are the bases of the Trapezoid
  • h is the height of the Trapezoid

Circle Formulas

Circumference-of-Circle

Where ‘r’ is the radius of a Circle

Cube Formulas

Surface-Area-of-Cube-(1)

Where ‘a’ is the length of the sides of the Cube

Cylinder Formulas

Surface-Area-of-Cylinder

Where

  • ‘r’ is the radius of base of Cylinder
  • ‘h’ is the height of Cylinder

Cone Formulas

Surface-Area-of-Cone

Where,

  • ‘r’ is radius of the base of Cone 
  • h is height of the Cone

Sphere Formulas

Surface-Area-of-Sphere

Where r is the radius of the Sphere

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 = √(length2 + breadth2)

Square
  • Perimeter = 4 × Side
  • Area = Side × Side
  • Diagonal = √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 = 2πr
  • Area = πr2

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 Cube = l × b × h

Cylinder
  • Curved Surface Area of Cylinder = 2πrh
  • Total Surface Area of Cylinder = 2πr(r + h)
  • Volume of Cylinder = V = πr2h

Cone
  • Curved Surface Area of a Cone = πrl
  • Total Surface Area of Cone = πr(r + l) = πr[r + √(h2 + r2)]
  • Volume of a Cone = V =1/2× πr2h

Sphere
  • Surface Area of a Sphere = 4πr2
  • Volume of a Sphere = 4/3 × πr3

Hemisphere
  • Curved Surface Area of a hemisphere = 2πr2
  • Surface Area of a hemisphere = 3πr2
  • Volume of a Sphere = 4/3 × πr3

Also, Check

Solved Examples on Geometry Formulas

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)=πr2

=>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 = 1/2× 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= 2πrh

=>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 – Basic Geometry Formulas

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, weight 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.

FAQs on Geometry Formulas

Who is father of geometry?

Euclid is considered to be father of geometry

What is basic geometry?

Basic geometry deals with concepts of point, line, angles and plane figures

What are the geometric shapes?

The basic geometric shapes are triangle, rectangle, square, parallelogram, rhombus, trapezium and circle

What are the types of geometry?

The different types of geometry are Euclidean, Non-Euclidean, Projective and Topology geometry

What are all geometry formulas?

All geometry formulas includes mathematical formulas for finding area, perimeter and volume of shapes

Where can I get all the geometry formulas?

You can get all the geometry formulas in this article by geeksforgeeks



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