# Here are some common formulas used in Geometry

#### There are many formulas in geometry, and they can be organized in different ways depending on the context.

Some common geometry formulas include:

1. Distance formula: used to find the distance between two points in a plane
• d = √((x2 – x1)^2 + (y2 – y1)^2)
2. Pythagorean theorem: used to find the length of the hypotenuse of a right triangle
• c^2 = a^2 + b^2
3. Perimeter and area formulas:
• Rectangle: P = 2l + 2w, A = lw
• Square: P = 4s, A = s^2
• Triangle: P = a + b + c, A = (1/2)bh
• Circle: C = 2πr, A = πr^2
• Trapezoid: A = (h/2) (a+b)
4. Volume formulas:
• Rectangular prism: V = lwh
• Cube: V = s^3
• Sphere: V = (4/3)πr^3
• Cylinder: V = πr^2h
• Cone: V = (1/3)πr^2h
5. Trigonometry Formulas :
• sine function: sin(x) = opposite side / hypotenuse
• cosine function: cos(x) = adjacent side / hypotenuse
• tangent function: tan(x) = opposite side / adjacent side
• angle addition formula : sin(x+y) = sinx cosy + cosx siny
• angle subtraction formula: sin(x-y) = sinx cosy – cosx siny
• double angle formula: sin 2x = 2sinxcosx, cos 2x = cos^2 x – sin^2 x

*Note: This is not the exhaustive list of all formulas, only some of the most common formulas were mentioned above.

#### Basics

Geometry is a branch of mathematics that deals with shapes, sizes, and positions of objects in space. The main concepts in geometry include points, lines, angles, circles, triangles, and other shapes. It also involves concepts of measurement, such as length, area, and volume. One of the main goals of geometry is to deduce relationships between figures using logic and reason.

In Euclidean geometry, geometric figures are defined using a set of axioms, and theorems are proven using logical deduction. Non-Euclidean geometry, on the other hand, involves the study of geometries in which the parallel postulate does not hold true. Some important branches of it includes Euclidean, Analytic, Transformational, Differential, and projective geometry.

It is used in many fields such as physics, engineering, computer graphics, and architecture. It is also an important component of the mathematics curriculum at many levels, from elementary school through college and university. It’s not just limited to pure mathematics, but also find application in many real-world problems.