2d And 3d Geometry Formulas - Pdf

3 min read Jul 07, 2024
2d And 3d Geometry Formulas - Pdf

2D and 3D Geometry Formulas

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and positions of objects. It involves the use of points, lines, angles, and planes to define various geometric figures. In this article, we will provide a comprehensive list of 2D and 3D geometry formulas that are commonly used in mathematics and physics.

2D Geometry Formulas


Points and Lines

  • Midpoint of a line segment: M = ((x1 + x2)/2, (y1 + y2)/2)
  • Distance between two points: d = √((x2 - x1)^2 + (y2 - y1)^2)
  • Slope of a line: m = (y2 - y1)/(x2 - x1)
  • Equation of a line: y = mx + c

Triangles

  • Area of a triangle: A = (b \* h)/2
  • Perimeter of a triangle: P = a + b + c
  • Semi-perimeter of a triangle: s = (a + b + c)/2

Circles

  • Circumference of a circle: C = 2πr
  • Area of a circle: A = πr^2

Quadrilaterals

  • Area of a rectangle: A = l \* w
  • Perimeter of a rectangle: P = 2(l + w)
  • Area of a parallelogram: A = b \* h
  • Perimeter of a parallelogram: P = 2(a + b)

3D Geometry Formulas


Points and Lines

  • Distance between two points: d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
  • Midpoint of a line segment: M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

Triangles

  • Area of a triangle: A = (b \* h)/2
  • Volume of a triangular prism: V = (A \* h)/3

Polyhedra

  • Volume of a cube: V = s^3
  • Volume of a rectangular prism: V = l \* w \* h
  • Surface area of a cube: SA = 6s^2
  • Surface area of a rectangular prism: SA = 2(lw + lh + wh)

Spheres

  • Surface area of a sphere: SA = 4πr^2
  • Volume of a sphere: V = (4/3)πr^3

Conclusion


In this article, we have provided a comprehensive list of 2D and 3D geometry formulas that are commonly used in mathematics and physics. These formulas are essential for solving problems involving points, lines, triangles, quadrilaterals, polyhedra, and spheres. We hope this article will serve as a valuable resource for students, teachers, and professionals who need to work with geometric shapes.

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