geometry formulas

Perimeter of polygons

P equals sum of all sides

Area of a parallelogram

a equals base times height

Area of a rhombus

A equals base times height

Area of a rectangle

a equals base times height

Area of a square

A equals base times height

Area of a triangle

A equals 1/2 base times height

Area of a trapezoid

A equals 1/2 (b1+b2)h

Area of a triangle without the height

A equals ½ ab sin c

Area of a circle

A equals p r2

Circumference of a circle

C= p x d

Arc length

A equals central angle over 360 times pi times D

Area of a sector

A equals central angle over 360 times pi times R2

Volume of a rectangular prism

V equals length times width times height

Volume of a cylinder

V equals pi R squared times H

Volume of a square pyramid

V equals 1/3 length times width times height

Volume of a cone

V equals 1/3 P squared times height

Density formula

Equals mass over volume

Population density

Population over area

Ratio of perimeter and sides

Perimeter one over perimeter two equals side one over side two

Ratio of area and sides

A1 over A2 equals side one squared over side two squared

Ratio of volume and sides

V1 one over V2 equals side one cubed overside two cubed

Scale factor formula

New value over the original value

Some of interior angles of a polygon

(N - 2) (180)

Exterior angle of a triangle

Interior plus interior equals the exterior angle

Rotational symmetry formula

360 divided by the number of sides

Right triangle proportion SAAS

Segment one over the altitude equals altitude over segment two

Right triangle proportion WLLS1

Whole hypotenuse over leg one equals leg one over segment one

Right triangle proportion WLLS2

Whole hypotenuse over leg two equals leg two over segment two

Sine of formula

Sin equals opposite over hypotenuse

Cosine formula

Cosine equals adjacent over hypotenuse

Tangent formula

Tan equals opposite over adjacent

Sin equals cosine

Sine plus cosine B equals 90

Pythagorean theorem

A squared plus B squared equals C squared

Triangle inequality theorem or when it gives you two sides of a triangle, but you have to find the third side

A+ B has to be greater than C

Median of a trapezoid

Median equals 1/2 base one plus base two

Slope intercept of a line

Y equals MX plus B

Point slope form of a line

Y minus Y1 equals M (X minus X1)

Slope, formula, parallel, verse perpendicular

Y2 minus Y1 over X2 minus X1

distance formula

D equals (x2-x1) squared plus (Y2-Y1) squared

Midpoint formula

(X1+ X2÷2, Y1+ Y2÷2)

Equation of a circle

(X2+ X ) squared + (Y2+y) squared

Central angle with the point at the center

Central angle equals the arc

Inscribed angle with the point on the circle

Inscribed angle equals 1/2 of the arc

Angles formed by chords with the vertex inside the circle

Angle equals big arc plus small arc divided by two

Area formed by tangent and secants with the point outside of the circle

Angle equals big arc minus small arc divided by two

Angles formed by the tangent and the radius

Make a 90° angle or a right triangle

Segment of intersecting chords

Segment one times segment two equals segment three times segment four

Segments of 2 secants

Whole secants times the outside equals whole secants times the other outside

Segment of tangent and secants

Tan squared equals whole secants times the outside

Common conversions to know

1000 cm3 equals 1 L