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