**Geometry Formulas: **Geometry formulas are essential for the calculation of various parameters such as dimension, perimeter, surface area and volume for various geometrical shapes.

Geometry is the study of the relationship between points, lines and angles, surfaces, dimensions and properties of an object. It is divided into two sub-disciplines: 2D (which includes plane geometry) and 3D (which includes solid geometry).

2D objects are flat objects that have only two dimensions: length and width. Examples of 2D objects include squares, circles and triangles.

3D objects are solid objects that have three dimensions: height or depth (cube, cuboid, sphere, cylinder and cone).

## What are Geometry Formulas?

2D and 3D geometry formulas are used to determine the size, shape, shape perimeter, shape area, shape surface area, shape volume, etc. 2D shapes include flat figures like squares, circle, triangle, etc. 3D shapes include cube, cuboid, sphere, cylinder, cone, etc. Here are the basic geometry formulas:

**Also Read:** Law of Exponent Rules and Examples

## Basics Geometry Formulas: Area and Volume

Below you will find a collection of 2D geometrical formulas for different geometrical shapes, along with selected formulas for the integration of the mathematical constant **π** (pi).

## Geometry Formulas Two-Dimensional Objects: Perimeter and Volume

Shape Name | Shape | Formula |
---|---|---|

Rectangle/Square | P = 2l + 2w A = lw | |

Parallelogram | P = 2a + 2b A = bh | |

Triangle | P = a + b + c A = 1/2 bh | |

Trapezoid | P = a1 + a2 + b1 + b2 A = 1/2 h(b1 + b2) | |

Circle | ||

Regular Polygon |

## Geometry Three-Dimensional Objects: Surface Area and Volume

Shape Name | Shape | Formula |
---|---|---|

Rectangular Box/Cube | V = lwh S.A = 2lw + 2wh + 2lh | |

Cone | V = 1/3 πr^{2}hS.A = πr ^{2} + πrs | |

Sphere | V = 4/3 πr^{3}S.A = 4πr ^{2} | |

Pyramid | B = ab (area of the base) s = height of the triangle face P = 2a + 2b (perimeter of the base) V = 1/3 Bh S.A. = 1/2 P s + B | |

Cylinder | V= πr^{2}hS.A = 2πr ^{2} + 2πrh | |

Right Prism | B = (area of the base) P = (perimeter of the base) S.A. = 2B + Ph V = Bh |

## Important Unit Conversions For Geometry Formulas

These conversions are fundamental for solving problems related to length, area, volume, mass, time, angles, and temperature in mensuration.

It’s important for students to understand how to convert between different units as they work with various mathematical and scientific concepts.

**Length:**

- 1 meter (m) = 100 centimeters (cm)
- 1 kilometer (km) = 1000 meters (m)
- 1 meter (m) = 1000 millimeters (mm)

**Area:**

- 1 square meter (m²) = 10,000 square centimeters (cm²)
- 1 hectare (ha) = 10,000 square meters (m²)

**Volume:**

- 1 cubic meter (m³) = 1000 liters (L)
- 1 cubic centimeter (cm³) = 1 milliliter (mL)

**Mass:**

- 1 kilogram (kg) = 1000 grams (g)
- 1 gram (g) = 1000 milligrams (mg)

**Time:**

- 1 minute = 60 seconds
- 1 hour = 60 minutes = 3600 seconds

**Angles:**

- 1 degree (°) = 60 minutes (‘)
- 1 minute (‘) = 60 seconds (”)

**Temperature:**

- Celsius to Fahrenheit: F = (9/5)C + 32
- Fahrenheit to Celsius: C = 5/9(F – 32)

## Some Solved Example On Geometry Formulae

**Example 1: **

Problem: Calculate the circumference and the area and of a circle by using geometry formulas if the radius of the circle is 21 units.

Solution:

To find the area and the circumference of the circle.

Given: Radius of a circle = 21 units

Using geometry formulas for circles,

Area of circle = π × r^{2}

= 3.142857 × 21^{2}

= 1385.44

Now for the circumference of the circle,

Using geometry formulas for circle,

Circumference of a Circle = 2πr

= 2(3.142857)(21)

= 131.95

**Example 2: **

Problem: What is the area of a rectangular park whose length and breadth are 90 m and 60 m respectively?

Solution:

To find the area of a rectangular park:

Given: Length of the park = 90 m

The breadth of the park = 60 m

Using the geometry formulas for a rectangle,

Area of Rectangle = (Length × Breadth)

= (90 × 60) m^{2}

= 5400 m^{2}