Geometric Formulas

Volume

100

Volume of a Cube

V=s³

200

Volume of a Prism

V=bh

300

Volume of a Pyramid

V=1/3bh

400

Volume of a Cone

V=1/3πr²h

500

Volume of a sphere

V=4/3πr³

Surface Area

100

Surface Area of a Right Prism

S=aP+Ph

200

Surface Area of a Right Cylinder

S=2πr²+2πrh

300

Surface Area of a Regular Pyramid

S=B+1/2Pl

(l= slant height)

400

Surface Area of a Sphere 

S=4πr²

500

Surface Area of a Right Cone

S=Πr²+Πrl

Area

100

Area of a Parallelogram 

A=bh

200

Area of a Triangle 

A=1/2bh

300

Area of a Trapezoid 

A=1/2h(b₁+b₂)

400

Area of a Rhombus 

A=1/2d₁d₂

500

Area of a Kite

A=1/2d₁d₂

Circles

100

Circumference of a Circle

C=Πd=2πr

200

Area of a Circle

A=2πr²

300

Area of a Regular Polygon

A=1/2aP=1/2a(ns)

400

Arc Length

Arc AB=mAB/360(2πr)

500

Area of a Sector

mAB/360(πr²)

Miscellaneous

100

Geometric Mean(Altitude)

POH1/alt. = alt./POH2

200

Geometric Mean (leg)

Hyp/leg = leg/POHadj

300

45-45-90 rules

If given leg, other leg is same measure, hypotenuse is square root of 2 as long as each leg

If given hypotenuse, divide by square root of 2 to find both legs

400

30-60-90 rules

If given 30 leg, multiply by the square root of 3 to find 60 leg, and by 2 to find hypotenuse 

If given 60 leg, divide by square root of 3 to find 30 leg. Then multiply 30 leg by 2 to find hypotenuse.

If given 90 leg, divide by 2 to find 30 leg, and multiply 30 leg by square root of 3 to find 60 leg

500

Sine, cosine, and tangent 

Sin=opp/hyp

Cos=adj/hyp

Tan=opp/adj