# Geometry Formulas

The geometry formulas are used for finding dimensions, perimeter, area, surface area, volume, etc. of the geometric shapes. Geometry is a part of mathematics that deals with the relationships of points, lines, angles, surfaces, solids measurement, and properties. There are two types of geometry: 2D or plane geometry and 3D or solid geometry. 2D shapes are flat shapes that have only two dimensions, length, and width as in squares, circles, and triangles, etc. 3D objects are solid objects, that have three dimensions, length, width, and height or depth, as in a cube, cuboid, sphere, cylinder, cone, Let us learn geometry formulas along with a few solved examples in the upcoming sections.

## What Are Geometry Formulas?

The formulas used for finding dimensions, perimeter, area, surface area, volume, etc. of 2D and 3D geometric shapes are known as geometry formulas. 2D shapes consist of flat shapes like squares, circles, and triangles, etc., and cube, cuboid, sphere, cylinder, cone, etc are some examples of 3D shapes. The basic geometry formulas are given as:

### List of Geometry Formulas

Below is the list of various geometry formulas for you according to the geometric shape.

- Perimeter of a Square = 4(Side)
- Perimeter of a Rectangle = 2(Length + Breadth)
- Area of a Square = Side
^{2} - Area of a Rectangle = Length × Breadth
- Area of a Triangle = ½ × base × height
- Area of a Trapezoid = ½ × \((base_1 + base_2)\) × height

Basic geometry formulas where the mathematical constant π is used are,

- Area of a Circle = A = π×r
^{2 } - Circumference of a Circle = 2πr
- The curved surface area of a Cylinder = 2πrh
- Total surface area of a Cylinder = 2πr(r + h)
- Volume of a Cylinder = V = πr
^{2}h - The curved surface area of a cone = πrl
- Total surface area of a cone = πr(r+l) = πr[r+√(h
^{2}+r^{2})] - Volume of a Cone = V = ⅓×πr
^{2}h - Surface Area of a Sphere = S = 4πr
^{2} - Volume of a Sphere = V = 4/3×πr
^{3}

where,

- r = Radius;
- h = Height. and,
- l = Slant height

The formula table depicts the geometry formulas used for different 2-D and 3-D shapes:

SHAPES | FORMULAS |

1. Right Triangle |
Pythagoras Theorem: a Area = ½ ab Perimeter = a + b + √(a Where, a = altitude of a triangle b = base of a triangle |

2. Triangle |
Perimeter, P = a + b + c Area, A = ½ bh Height, h = 2(A/b) Where, a,b,c are the sides of a triangle. |

3. Rectangle |
Perimeter = 2(l + w) Area = lw Diagonal, d = √(l Where, l = length of a rectangle w = width of a rectangle |

4.Parallelogram |
Perimeter, P = 2(a + b) Area, A = bh Height, h = A/b Base, b = A/h Where, a and b are the sides of a parallelogram h = height of a parallelogram |

5. Trapezium |
Area, A = ½(a + b)h Height, h = 2A/(a + b) Base, b = 2(A/h) – a Where, a and b are the parallel sides h = distance between two parallel sides |

6. Circle |
Circumference = 2πr Area = πr Diameter = 2r Where, r = radius of a circle |

7. Square |
Perimeter, P = 4a Area, A = a Diagonal, d = a√2 Side, a = √A = d/2√2 Where, a = side of a square |

8. Arc |
Arc Length, L = rθ Area, A = ½r Here, θ is the central angle is radians. Where, r = radius |

9. Cube |
Area, A = 6a Volume, V = a Edge, a = V Space diagonal = a√3 Where, a = side of a cube |

10. Cuboid |
Surface Area, A = 2(lb + bh + hl) Volume, V = lbh Space diagonal, d = √( l Where, l= length b= breath h= height |

11. Cylinder |
Total Surface Area, A = 2πrh + 2πr Curved Surface Area, A Volume, V = πr Base Area, A Radius, r = √(V/πh) Where, r= radius of a cylinder h= height of a cylinder |

12. Cone |
Total Surface Area, A = πr(r+l) = πr[r+√(h Curved Surface Area, A Volume, V = ⅓πr Slant Height, l = √(h Base Area, A Where, r= radius of a cone h= height of a cone l = slant height |

13. Sphere |
Surface Area, A = 4πr Volume, V = ⁴⁄₃πr Diameter = 2r Where, r= radius of a sphere |

Let's have a look at solved examples to understand geometry Formulas better.

## Solved Examples Using Geometry Formulas

Example 1: 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 circle,

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

**Answer: The area of a circle is 1385.44 sq. units and the circumference of a circle is 131.95 units.**

**Example 2:** What is the area of a rectangular park whose length and breadth are 60m and 90m respectively?

**Solution:**

To find the area of a rectangular park:

Given: Length of the park = 60m

The breadth of the park = 90m

Using geometry formulas for rectangle,

Area of Rectangle = (Length × Breadth)

= (60 × 90) m^{2}

= 5400 m^{2}

**Answer: The area of the rectangular park is 5400 m ^{2}.**

**Example 3:** Using geometry formulas of the cube, calculate the surface area and volume of a cube whose edge is 6 units respectively?

**Solution:**

To Find: The surface area and volume of a cube whose edge is 6 units

Using geometry formulas of cube,

Surface area of cube is = A = 6a^{2}

A = 6 (6)^{2}

A = 6 × 36 = 216 units^{2}

Volume of a cube, V = a^{3}

V = (6)^{3}

V = 216 units^{3}

**Answer: The surface area of the cube is 216 units ^{2}. The volume of the cube is 216 units^{3}**

## FAQ's on Geometry Formulas

### What Are the Geometry Formulas of a Cuboid?

The geometry formulas of a cuboid are listed below:

- Surface Area of cuboid, A = 2(lb + bh + hl)
- Volume of cuboid, V = lbh
- Space diagonal of cuboid, d = √(l
^{2}+ b^{2}+h^{2})

Where,

- l= length
- b= breadth
- h= height

### What Are the Geometry Formulas of a Rectangle?

The geometry formulas of a rectangle are listed below:

- Perimeter of a rectangle = 2(l + w)
- Area of rectangle = lw
- Diagonal of a rectangle, d = √(l
^{2}+ w^{2})

Where,

- l = length of a rectangle
- w = width of a rectangle

### What Are the Geometry Formulas of a Cone?

The geometry formulas of a cone are listed below:

- Total surface area of cone, A = πr(r+l) = πr[r+√(h
^{2}+r^{2})] - Curved surface area of cone, A
_{c}= πrl - Volume of cone, V = ⅓πr
^{2}h - Slant Height of cone, l = √(h
^{2}+r^{2}) - Base Area, A
_{b}= πr^{2}

Where,

- r= radius of a cone
- h= height of a cone
- l = slant height

### What Are the Geometry Formulas of a Circle?

The geometry formulas of a circle are listed below:

- Circumference = 2πr
- Area = πr
^{2} - Diameter = 2r

Where, r = radius of a circle