Geometry Unit 11 formula study guide

Prism Surface Area Formula

LA=PH

SA=LA+2b

Cylinders Surface Area Formula

LA=2πrh

SA=LA + 2πr²

Pyramids Surface Area Formula

LA = ½ Pl

SA = LA + B

Cones surface area formula

LA= πrl

SA= LA + πr²

Meaning of l

Slant height

Meaning of B

Area of the base

Meaning of H

Height of the figure

Meaning of h

Height of the base

Prisms Volume Formula

V=BH

Pyramids Volume Formula

V= 1/3 BH

Cylinder volume formula

V=BH

B= πr²

V= πr²H

Cones Volume Formula

V= 1/3 BH

B= πr²

V= 1/3πr²H

Sphere Surface Area formula

SA= 4πr²

Sphere Volume Formula

V= 4/3 πr³

Hemisphere surface area formula

SA= 3πr²

Hemisphere Volume Formula

V= 2/3πr³

(Half of regular sphere volume)

Triangle area formula

A= ½ bh

Square area formula

s = side

A= s²

Rectangle Area Formula

A= lw

l= Length

w= Width

Circle circumference and area formulas

C= 2πr OR πd

A= πr²

Parallelogram area formula

A= bh

Trapezoid area formula

A= ½ h( b1 + b2 )

Pythagorean theorem

a² + b² = c²

Composite Figure

A figure than can be split into 2 or more shapes

Area of a regular polygon

A = ½ ap

a= apothem p= perimeter

Steps of solving a regular polygon

n= total number of sides s= Central angle a= apothem p= perimeter A= area

1) Find central angle: 360÷n. 2) s÷2. 3) find if its a 30-60-90, 45-45-90, or SOHCAHTOA triangle

4) Find a 5) Find p. 6) Find Area Area= ½ ap

Scale factor ratio

a/b OR a:b

Surface area ratio

a²/b²

Volume ratio

a³/b³

Changing dimensions

If dimensions are multiplied by a scale factor of K

Then surface area is k² times the original surface area

The volume is k³ times the original volume