Geometry Formulas : Geometry formulas play a crucial role in calculating various attributes such as dimensions, perimeter, area, surface area, and volume for different geometric shapes. Geometry is a branch of mathematics dedicated to understanding the relationships between points, lines, angles, surfaces, measurements, and properties of objects. This discipline is divided into two categories: 2D, which encompasses plane geometry, and 3D, which involves solid geometry.
2D shapes consist of flat figures possessing only two dimensions—length and width. Examples include squares, circles, and triangles. Conversely, 3D objects are solid entities with three dimensions—length, width, and height or depth. Examples comprise cubes, cuboids, spheres, cylinders, and cones.
Also Check – Sets Formula
What are Geometry Formulas?
Geometry formulas are employed to calculate dimensions, perimeter, area, surface area, volume, and other attributes of both 2D and 3D geometric shapes. 2D shapes encompass flat figures such as squares, circles, and triangles. On the other hand, examples of 3D shapes include cubes, cuboids, spheres, cylinders, and cones. The fundamental geometry formulas are outlined below:
Also Check – Ratio and Proportion Formula
Basic Geometry Formulas
Presented below are a range of 2D geometry formulas pertaining to distinct geometric shapes, accompanied by select formulas integrating the mathematical constant π (pi).
Formulas for 2D Geometry:
- Perimeter of a Square = 4 × Side
- Perimeter of a Rectangle = 2 × (Length + Breadth)
- Area of a Square = Side²
- Area of a Rectangle = Length × Breadth
- Area of a Triangle = ½ × Base × Height
- Area of a Trapezoid = ½ × (Base₁ + Base₂) × Height
- Area of a Circle = A = π × r²
- Circumference of a Circle = 2πr
Moving on to the realm of 3D geometry, the fundamental formulas are enumerated below, featuring the incorporation of the mathematical constant π.
Also Check – Factorization Formula
Formulas for 3D Geometry:
- Curved Surface Area of a Cylinder = 2πrh
- Total Surface Area of a Cylinder = 2πr(r + h)
- Volume of a Cylinder = V = πr²h
- Curved Surface Area of a Cone = πrl
- Total Surface Area of a Cone = πr(r + l) = πr[r + √(h² + r²)]
- Volume of a Cone = V = ⅓ × πr²h
- Surface Area of a Sphere = S = 4πr²
- Volume of a Sphere = V = 4/3 × πr³
Herein,
r denotes Radius,
h signifies Height, and
l represents Slant height.
Download PDF Geometry Formulas
The provided table showcases formulas for both 2D and 3D geometry.
| SHAPES | FORMULAS |
|---|---|
| 1. Right Triangle | Pythagoras Theorem: base2 + height2 = hypotenuse2
Area = ½ × base × height Perimeter = base + height + hypotenuse |
| 2. Triangle | Perimeter, P = a + b + c
Where, a, b, and c are the sides of a triangle. Area, A = ½ base × height |
| 3. Rectangle | Perimeter = 2(l + w)
Area = lw Diagonal, d = √(l2 + w2) Where, l = length of a rectangle w = width of a rectangle |
| 4.Parallelogram | Perimeter, P = 2(a + b)
Where, a and b are the sides of a parallelogram Area of parallelogram, A = base × height Height, h = Area/base Base, b = Area/height |
| 5. Trapezium | Area, A = ½(a + b)h
Where, a and b are the parallel sides h = distance between two parallel sides |
| 6. Circle | Circumference = 2πr
Area = πr2 Diameter = 2r Where, r = radius of a circle |
| 7. Square | Perimeter, P = 4a
Area, A = a2 Diagonal, d = a√2 Side, a = √A Where, a = side of a square |
| 8. Arc | Arc Length, L = rθ
Here, θ is the central angle in radians and r = radius |
| 9. Cube | Area, A = 6a2
Volume, V = a3 Edge, a = Volume⅓ 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 = √( l2 + b2 +h2) Where, l= length b= breadth h= height |
| 11. Cylinder | Total Surface Area, A = 2πrh + 2πr2
Curved Surface Area, Ac = 2πrh Volume, V = πr2h Base Area, Ab = πr2 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+√(h2+r2)]
Curved Surface Area, Ac = πrl Volume, V = ⅓πr2h Slant Height, l = √(h2+r2) Base Area, Ab = πr2 Where, r= radius of a cone h= height of a cone l = slant height |
| 13. Sphere | Surface Area, A = 4πr2
Volume, V = ⁴⁄₃πr3 Diameter = 2r Where, r= radius of a sphere |
Below, you'll find the geometry formulas specific to a cuboid:
Surface Area of a Cuboid, A = 2(lb + bh + hl)
Volume of a Cuboid, V = lbh
Space Diagonal of a Cuboid, d = √(l² + b² + h²)
In this context:
l stands for length
b stands for breadth
h stands for height
Geometry formulas serve as valuable tools for calculating the perimeter, area, volume, and surface areas of both 2D and 3D geometric shapes. In our everyday experiences, we encounter a multitude of objects that possess resemblances to various geometric figures. These formulas enable us to determine the areas and volumes of these geometric entities in practical applications.
The geometry formulas of a circle are listed below:
Circumference = 2πr
Area = πr2
Diameter = 2r
Where, r = radius of a circle
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 = √(l2 + w2)
Where,
l = length of a rectangle
w = width of a rectangle
