Geometry Basic

 

Basic Geometry:

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:

Formulas for 2D Geometry:

1. Perimeter of a Square = 4 × Side

2. Perimeter of a Rectangle = 2 × (Length + Breadth)

3. Area of a Square = Side²

4. Area of a Rectangle = Length × Breadth

5. Area of a Triangle = ½ × Base × Height

6. Area of a Trapezoid/ Trapezium= ½ × (Base₁ + Base₂) × Height

Area, A = ½(a + b)h

Where,

a and b are the parallel sides

h = distance between two parallel sides

7. Area of a Circle = A = π × r²

8. Circumference of a Circle = 2πr

9. Area of a rhombus A= 1/2 d1× d2

10. Area of a kite A= 1/2 d1 × d2

11. Area of equilateral triangle= 

√3/4 a square

12. Area of an isosceles triangle = b/4 √(4 a square - b square) ( a= length of equal sides, b= unequal side

*Pie, π= 3.141

9. Perimeter of a Parallelogram

 P = 2(a + b)

Where, a and b are the sides of a parallelogram

10. Area of parallelogram, A = base × height

Here, Height=  h

 Base= b

11. Pythagoras Theorem: base2 + height2 = hypotenuse2

Formulas for 3D Geometry:

1. Curved Surface Area of a Cylinder = 2πrh

2. Total Surface Area of a Cylinder = 2πr(r + h)

3. Volume of a Cylinder = V = πr²h

4. Curved Surface Area of a Cone = πrl

5. Total Surface Area of a Cone = πr(r + l) = πr[r + √(h² + r²)]

6. Volume of a Cone = V = ⅓ × πr²h

7. Surface Area of a Sphere = S = 4πr²

8. Volume of a Sphere = V = 4/3 × πr³

9. Surface Area of a Cuboid, A = 2(lb + bh + hl)

10. Volume of a Cuboid, V = lbh

11. Surface area of Cube = 6a2

Volume of a cube, V = a3

Space diagonal = a√3

a = side of a cube

12. Space Diagonal of a Cuboid, d = √(l² + b² + h²)

In this context:

l stands for length

b stands for breadth

h stands for height

Happy learning with Noor @Hopeland