Geometry

Point

Dimensionless geometric figure having only location

Line

Shortest distance between any two points

Angle

Opening between two lines or planes that meet

Vertex

Point where two lines meet

Acute Angle

Angle between 0 and 90 degrees

Right Angle

Angle equal to 90 degrees

Obtuse Angle

Angle between 90 and 180 degrees

Straight Angle

Angle equal to 180 degrees

Reflex Angle

Angle between 180 and 360 degrees

Full Revolution

360 degrees, 2pi radians, 400 grads, or 6400 mils

Polygon

2D closed plane figure with a finite number of sides

Sum of Interior Angles of Polygon

S = (n – 2) * 180 degrees

Interior Angle of Regular Polygon

theta = [(n – 2) * 180] / n

Sum of Exterior Angles of Polygon

S = 360 degrees

Exterior Angle of Regular Polygon

beta = 360 / n

Number of Diagonals in Polygon

ND = (n / 2) * (n – 3)

Area of Regular Polygon (side a)

A = (1/4) * n * a^2 * cot(180/n)

Area of Polygon circumscribing circle

A = n * r^2 * tan(180/n)

Area of Polygon inscribed in circle

A = (1/2) * n * r^2 * sin(360/n)

Triangle Area (base and height)

A = (1/2) * b * h

Triangle Area (SAS)

A = (1/2) * a * b * sin(theta)

Semiperimeter (s)

s = (a + b + c) / 2

Heron's Formula

Area = sqrt(s * (s – a) * (s – b) * (s – c))

Triangle Area with Incircle

Area = r * s

Triangle Area with Circumcircle

Area = (abc) / (4R)

Square Area

A = a^2

Rectangle Area

A = a * b

Rhombus Area

A = (1/2) * d1 * d2 or A = a^2 * sin(theta)

Parallelogram Area

A = b * h or A = a * b * sin(theta)

Trapezoid Area

A = (1/2) * (b + B) * h

Circle Circumference

C = 2 * pi * r

Circle Area

Area = pi * r^2

Arc Length (theta in radians)

s = r * theta

Arc Length (theta in degrees)

s = 2 * pi * r * (theta / 360)

Sector Area (theta in radians)

Area = (1/2) * r^2 * theta

Sector Area (theta in degrees)

Area = (pi * r^2 * theta) / 360

Segment Area

Area = Area of Sector – Area of Triangle

Cube Volume

V = a^3

Cube Surface Area

AS = 6 * a^2

Rectangular Prism Volume

V = L * W * H

Sphere Volume

V = (4/3) * pi * r^3

Sphere Surface Area

AS = 4 * pi * r^2

Cone Volume

V = (1/3) * pi * r^2 * h

Cone Surface Area

AS = pi * r^2 + pi * r * L