Basic Geometry Formulas
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.
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 own distinct formula. These formulas are listed below.
Square Formulas
Various square formulas are,
- Perimeter of Square = 4a
- Area of Square = a2
Where ‘a’ is the length of the sides of a square
Rectangle Formulas
Various rectangle formulas are,
- Perimeter of Rectangle = 2(l + b)
- Area of Rectangle = l × b
Where ‘l’ is Length and ‘b’ is Breadth
Triangle Formulas
Various triangle formulas are,
- Perimeter of Triangle = Sum of All Sides
- Area of Triangle = 1/2 × b × h
Where,
- ‘b’ is the base of the triangle
- ‘h’ is the height of the triangle
Trapezoid Formulas
- Area of Trapezoid (A) = 1/2 × (b1 + b2) × h
Where,
- b1 and b2 are the bases of the Trapezoid
- h is the height of the Trapezoid
Circle Formulas
- Area of Circle = π × r2
- Circumference of Circle(C) = 2πr
Where ‘r’ is the radius of a Circle
Cube Formulas
- Surface Area of Cube = 6a2
- Volume of Cube = a3
Where ‘a’ is the length of the sides of the Cube
Cylinder Formulas
- Curved Surface Area of Cylinder = 2πrh
- Total Surface Area of Cylinder = 2πr(r + h)
- Volume of Cylinder = V = πr2h
Where
- ‘r’ is the radius of base of Cylinder
- ‘h’ is the height of Cylinder
Cone Formulas
- 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
Where,
- ‘r’ is radius of the base of Cone
- h is height of the Cone
Sphere Formulas
- Surface Area of a Sphere = 4πr2
- Volume of a Sphere = 4/3 × πr3
Where r is the radius of the Sphere
2D Geometry Formulas
The geometry formulas for 2D shapes are tabulated below:
2D Shape |
Formulas |
---|---|
Triangle |
|
Rectangle |
|
Square |
|
Parallelogram |
|
Rhombus |
|
Trapezium |
|
Circle |
|
3D Geometry Formulas
The geometry Formulas for 3D figures are mentioned below:
3D Shape |
Formulas |
---|---|
Cube |
|
Cuboid |
|
Cylinder |
|
Cone |
|
Sphere |
|
Hemisphere |
|
Also, Check
Sample Problems 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
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 w3wiki
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