The Sum of the Interior Angles of a Polygon:

= ( The Number of Sides - 2 ) * 180

The Area of a Square:

= Side * Side = Side^2

The Area of a Rectangle:

= Length * Width

The Area of a Trapezoid:

= ( Base_1 + Base_2 ) / 2 * Height

The Area of a Parallelogramm:

= Base * Height

The Triangle Inequality Law:

If you are given two sides of a triangle, the length of the third side must lie between the difference and the sum of the two given sides.

The Pythagorean Theorem:

A^2 + B^2 = C^2

The Three Most Common Right Triangles:

- 3-4-5

- 5-12-13

- 8-15-17

The Isosceles Right Triangle:

- Leg_1: 45° - X

- Leg_2: 45° - X

- Leg_3: 90° - X * Square Root of 2

The 30°-60°-90° Triangle:

- Leg_1: 30° - X

- Leg_2: 60° - X * Square Root of 3

- Leg_3: 90° - 2X

The Area of a Triangle:

= ( Base * Height ) / 2

The Diameter of a Circle:

= 2 * Radius

The Circumference of a Circle:

= Pi * Diameter = Pi * ( 2 * Radius )

Pi:

Ca. 3.14 or respectively ca. 22 / 7.

The Area of a Circle:

= Pi * Radius^2

The Inscribed Angle:

An inscribed angle is equal to half the angle of the arc it intercepts.

The Volume of a Cylinder:

= Pi * Radius^2 * Height

The Slope of a Line:

= Rise / Run = ( Y_2 - Y_1 ) / ( X_2 - X_1 ) = ( Y_1 - Y_2 ) / ( X_1 - X_2 )

The Four Types of Slopes:

1. Positive Slope

2. Negative Slope

3. Zero Slope

4. Undefined Slope

The Slope Intercept Equation:

Y = M * X + B

How to Calculate the Distance Between Two Points in the Coordinate Plane?

You can use the Pythagorean Theorem to do so.

The Area of a Rhombus:

= ( Diagonal_1 / Diagonal_2 ) / 2

The Area of an Equilateral Triangle:

An equilateral triangle is a triangle with three sides of equal length.

The equilateral triangle has a base of length X and a height of length ( X / 2 * Square Root of 3 ).

Therefore, the area of an equilateral triangle with a side length of X is equal to X * ( X / 2 * Square Root of 3 ) / 2 = ( X^2 * Square Root of 3 ) / 4.

The Diagonal of a Square:

= X * Square Root of 2

The Main Diagonal of a Cube:

= X * Square Root of 3

How to Find the Diagonal of a Rectangle?

If you know the length and the width of a rectangle, you can use the Pythagorean Theorem to solve for the length of the diagonal.

How to Find the Main Diagonal of a Rectangular Solid?

You can find the main diagonal of a rectangular solid by using the Pythagorean Theorem twice.

The Total Surface Area of a Cylinder:

= ( 2 * Area of the Circle ) + ( Circumference of the Circle ) * Height of the Cylinder = ( 2 * Pi * Radius^2 ) + ( Pi * Radius * 2 ) * Height

The Slope of Parallel Lines:

Parallel lines have equal slopes: M_1 = M_2.

The Slope of Perpendicular Lines:

Perpendicular lines have negative reciprocal slopes: M_2 = ( -1 ) * ( 1 / M_1 ).

The Midpoint Between the Two Points ( X_1 , Y_1 ) and ( X_2 , Y_2):

= ( ( X_1 + X_2 ) / 2 , ( Y_1 + Y_2 ) / 2 )

The Quadratic Formula:

X_1,2 = ( - B +- Square Root of ( B^2 - 4 * A * C) ) / 2 * A

The Quadratic Function:

A * X^2 + B * X + C = 0

The Perimeter of a Square:

= Side + Side + Side + Side = 4 * Side

The Perimeter of a Rectangle:

= Length + Length + Width + Width = 2 * Length + 2 * Width

The Perimeter of a Triangle:

= Side_1 + Side_2 + Side_3

The Perimeter of a Parallelogramm:

= Length + Length + Width + Width = 2 * Length + 2 * Width

The Volume of a Rectangular Solid:

= Length * Width * Height

The Surface Area of a Rectangular Solid:

= 2 * ( Length * Width ) + 2 * ( Length * Height ) + 2* ( Width * Height )

The Volume of a Cube:

= Side * Side * Side = Side^3

The Surface Area of a Cube:

= 6 * Side^2