Basic Geometry Formulas

In mathematics, geometry stands as a discipline of study and is a subject for the analysis of shapes and structures along with their properties. Geometry formulas are used for finding dimensions, perimeter, area, surface area, volume, etc. of the geometric shapes.

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.

The article below illustrates the standard and derived formulas of geometry for the calculation of various parameters of a particular shape. These formulas determine the unknown volume, area, perimeter, length of sides and diagonals, etc.

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

Various circle formulas are:

• Area of Circle = π × r²
• Circumference of Circle(C) = 2πr

Where ‘r’ is the radius of a Circle

Cube Formulas

Various Cube formulas are:

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

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

Cylinder Formulas

Various Cylinder formulas are:

• 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

Various Cone formulas are:

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

3D Geometry Formulas

The geometry Formulas for 3D figures are mentioned below:

Also Check:

• Geometric Shapes
• Geometry Questions
• Applications of Geometry

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.

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

Conclusion

The basic geometry formulas are foundational tools in mathematics that aid in solving problems involving shapes and their properties. Mastering these formulas not only enhances your understanding of the geometry but also builds a strong foundation for the advanced mathematical concepts. Whether we're calculating areas, perimeters or volumes these formulas are essential in both the academic and real-world applications.