Circumference of a circle:
Circumference = diameter x pi

Areas

Area of a square:
Area = length x width, or length of one side squared

Area of a rectangle:
Area = length x width

Area of a triangle:
Area = 0.5 x base x perpendicular height

Area of a pentagon:
Area = square of the length of one side x 1.720

Area of a hexagon:
Area = square of the length of one side x 2.598

Area of an octagon:
Area = square of the length of one side x 4.828

Area of a cube:
Area = square of the length of one side x 6

Area of a sphere:
Area = square of the diameter x pi

Area of a circle:
Area = square of the radius x pi

Area of an ellipse:
Area = long diameter x short diameter x 0.7854

Volumes

Volume of a cube:
Volume = cube of the length of one side

Volume of a pyramid:
Volume = area of the base x height x (1/3)

Volume of a cylinder:
Volume = square of the radius of the base x pi x height

Volume of a sphere:
Volume = cube of the radius x pi x (4/3)

Volume of a cone:
Volume = square of the radius of the base x pi x height x (1/3)

Volume of a rectangular solid:
Volume = length x width x height

Triangles

Pythagorean theorem:
The square of the hypotenuse of a right-angled triangle is
equal to the sum of the squares of the other two sides

Law of Sines: (refer to diagram)
In any triangle, a/sinA = b/sinB = c/sinC

Right triangles: (refer to diagram)
a = c x sinA = b x tanA
b = c x cosA = a x cotA
c = a x cosecA = b x secA

For all triangles:
The sum of the angles of a triangle = 180 degrees.

Given two sides (b and c) and one angle (A),
a = square root of (b^2 + c^2 - 2 x b x c x cosA )

Given two angles (A and B) and one side (A),
a = b x sinA/sinB
c = b x sinC/sinB

Given three sides (a, b, and c),
cosA = (b^2 + c^2 - a^2)/2bc
sinB = b/a x sinA

```        B
/|
/ |
/  |
c/   |a
/    |
/    _|
/__b_|_|
A        C```

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