2D and 3D Geometry Formulas in Hindi
What is Geometry?
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 describe and analyze geometric figures.
2D Geometry Formulas
Lines and Angles
- Perpendicular Lines: Two lines are said to be perpendicular if they intersect at a right angle (90°).
- Parallel Lines: Two lines are said to be parallel if they never intersect, no matter how far they are extended.
- ** Angle Sum Property:** The sum of interior angles of a polygon is equal to (n-2) * 180°, where n is the number of sides.
Triangles
- Area of a Triangle: The area of a triangle is given by (base * height) / 2.
- Perimeter of a Triangle: The perimeter of a triangle is the sum of all its sides.
- Pythagorean Theorem: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
Quadrilaterals
- Area of a Rectangle: The area of a rectangle is given by length * breadth.
- Perimeter of a Rectangle: The perimeter of a rectangle is 2 * (length + breadth).
- Area of a Square: The area of a square is given by side * side.
Circles
- Circumference of a Circle: The circumference of a circle is given by 2 * π * radius.
- Area of a Circle: The area of a circle is given by π * radius * radius.
- Sector Area: The area of a sector is given by (angle/360) * π * radius * radius.
3D Geometry Formulas
Points, Lines, and Planes
- Distance Formula: The distance between two points (x1, y1, z1) and (x2, y2, z2) is given by √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2).
- Section Formula: The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Polyhedra
- Surface Area of a Cube: The surface area of a cube is given by 6 * side * side.
- Volume of a Cube: The volume of a cube is given by side * side * side.
- Surface Area of a Rectangular Prism: The surface area of a rectangular prism is given by 2 * (length * breadth + breadth * height + length * height).
- Volume of a Rectangular Prism: The volume of a rectangular prism is given by length * breadth * height.
Spheres and Cones
- Surface Area of a Sphere: The surface area of a sphere is given by 4 * π * radius * radius.
- Volume of a Sphere: The volume of a sphere is given by (4/3) * π * radius * radius * radius.
- Slant Height of a Cone: The slant height of a cone is given by √(radius^2 + height^2).
- Surface Area of a Cone: The surface area of a cone is given by π * radius * (radius + slant height).
- Volume of a Cone: The volume of a cone is given by (1/3) * π * radius * radius * height.
These are some of the important formulas in 2D and 3D geometry. Mastering these formulas can help you solve complex problems in geometry and other branches of mathematics.
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