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
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c/ |a
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A C