three dimensional figures

polyhedron

all the faces are polygons

face

a side of a 3d shape

examples of polyhedrons

cube,prism,pyramid

Euler formula

F + V = E+ 2

lateral faces

up down

bases

usually bottom top

prism property

the bases of a prism are congruent

surface area

sum of the areas of all the faces of a solid

formula for every 3d shape SA

SA = LA+ BA

base and height are always

perpendicular

formula for prism SA

SA = Ph + 2B

formula for cylinder SA

SA = 2(pi)rh+ 2(pi)r²

pyramid surface area formula

SA = ½ pl + b

l

slant

formula for cone SA

SA = (pi)rl + (pi)r²

to find the surface area of two combined objects you

find the la of both separately and the base area of the bottom figure, then you add

to find the volume of two combined objects you

find the volume seperatly then combine

how to find apothem

$$a = \frac

if the scale factor of two similar solids is a/b, then the ratio for the perimeter is

a/b

if the scale factor of two similar solids is a/b, then the ratio for the surface area is

a²/b²

if the scale factor of two similar solids is a/b, then the ratio for the volume is

a³/b³