1.  Diagonal of an isosceles trapezoid if you know sides (leg and bases)  

Diagonal isosceles trapezoid abc

 

a , b     -  bases

c black   -  leg (lateral side)

d blue1   -  diagonal

 

Find the diagonal of an isosceles trapezoid if given all sides ( d blue1 ) :

Diagonal isosceles trapezoid abc F

 

 

2.  Diagonal of an isosceles trapezoid using the law of cosines  

Diagonal isosceles trapezoid cos

 

a , b     -  bases

c black   -  leg (lateral side)

d blue1   -  diagonal

alpha orange , beta brown     -  angles  at the base

 

Calculate the diagonal of a trapezoid if given base, lateral side and angle between them ( d blue1 ) :

Diagonal isosceles trapezoid cos F1

Diagonal isosceles trapezoid cos F2

 

Diagonal isosceles trapezoid cos F3

Diagonal isosceles trapezoid cos F4

 

 

3.  Diagonal of an isosceles trapezoid if you know height, midsegment, area of a trapezoid and angle between the diagonals    

Diagonal isosceles trapezoid Smh

a , b     -  bases

d blue1    -  diagonal

alpha orange , beta brown     -  angles between the diagonals

h  - height

m12 red  - midsegment

A18 black  - area

Calculate the diagonal of a trapezoid if given height, midsegment, area of a trapezoid and angle between the diagonals  ( d blue1 ) :

Diagonal isosceles trapezoid Smh F1

Diagonal isosceles trapezoid Smh F2

Diagonal isosceles trapezoid Smh F31

Diagonal isosceles trapezoid Smh F32

Diagonal isosceles trapezoid Smh F33

 

* It is true in this case:

Diagonal isosceles trapezoid Smh F4

 

 

4.  Diagonal of an isosceles trapezoid if you know height, sides and angle at the base  

Diagonal isosceles trapezoid h

a black  - lower base

b black  - upper base

c black   -  leg (lateral side)

d blue1  -  diagonal

alpha orange   -  angle at the base

h  - height

Calculate the diagonal of a trapezoid if given height, sides and angle at the base  ( d blue1 ) :

Diagonal isosceles trapezoid h F1

Diagonal isosceles trapezoid h F2

Diagonal isosceles trapezoid h F3



 

 


1.  Median of an isosceles trapezoid (also known as midline or midsegment) if you know bases  

middle line isosceles trapezoid ab

 

a , b     -  bases

m12 red  - midline

 

 

Find the midline of a trapezoid if given bases ( m red ) :

middle line isosceles trapezoid ab F

 

 

2.  Median of an isosceles trapezoid (also known as midline or midsegment), if you know base, height and angles at the base  

middle line isosceles trapezoid h

a black  - lower base

b black  - upper base

c black    -  leg (lateral side)

alpha orange   -  angle at the base

h  - height

m12 red  - midline

 

Find the median of a trapezoid if given base, height and angles at the base ( m red ) :

middle line isosceles trapezoid h F1

middle line isosceles trapezoid h F2

middle line isosceles trapezoid h F3

middle line isosceles trapezoid h F4

 

 

3.  Median of an isosceles trapezoid (also known as midline or midsegment), if you know diagonal, height and angle between the diagonals   

middle line isosceles trapezoid d

 

d blue1  -  diagonal

alpha orange , beta brown     -  angles between the diagonals

h  - height

m12 red  - midline

 

Find the median of a trapezoid if given diagonal, height and angle between the diagonals ( m red ) :

middle line isosceles trapezoid d F

 

 

4.  Median of an isosceles trapezoid (also known as midline or midsegment), if you know area of a trapezoid and height or lateral side and angle at the base  

middle line isosceles trapezoid S

A18 black  - areaof a trapezoid

c black    -  leg (lateral side)

h  - height

alpha orange   -  angle at the base

m12 red  - midline

 

Find the median of a trapezoid if given area of a trapezoid and height or lateral side and angle at the base ( m red ) :

middle line isosceles trapezoid S F1   middle line isosceles trapezoid S F2



 

 


1.  Height of an isosceles trapezoid if you know only sides or sides and angle at the base  

height isosceles trapezoid abcd

a , b   -  bases

c black   -  leg (lateral side)

alpha red1  -  angle  at the base

h  - height

 

Calculate the height of a trapezoid if given all sides (bases and leg) ( h ) :

height isosceles trapezoid abcd F1

 

Calculate the height of a trapezoid if given lateral side (leg) and angle at the base ( h ) :

height isosceles trapezoid abcd F21

height isosceles trapezoid abcd F22

 

 

2.  Height of an isosceles trapezoid if you know diagonal, angle between the diagonals and bases or midline  

height isosceles trapezoid d

a , b     -  bases

d blue1    -  diagonals

alpha orange , beta brown   -  angles between the diagonals

m12 red  - midline

h  - height

 

Calculate the height of a trapezoid if given diagonal, bases and angle between the diagonals ( h ) :

height isosceles trapezoid d F1

 

Calculate the height of a trapezoid if given diagonal, midline and angle between the diagonals ( h ) :

height isosceles trapezoid d F2

 

 

3.  Height of an isosceles trapezoid if you know area of a trapezoid  

height isosceles trapezoid S

a , b     -  bases

A18 black      -  area

m12 red  - midline

h  - height

 

Calculate the height of a trapezoid if given area and midline or bases ( h ) :

height isosceles trapezoid S F1   height isosceles trapezoid S F2



 

 


1.  Side (base) of a right trapezoid if you know other base and midline of a trapezoid  

length bases rectangular trapezoid m

 

a , b     -  bases

m red  - midline

 

 

Calculate the side of a trapezoid if given middle line and other base  ( a b  ) :

length bases rectangular trapezoid m F1    length bases rectangular trapezoid m F2

 

 

2.  Sides (bases) of a right trapezoid if you know lateral sides, angle at the base and other base  

length bases rectangular trapezoid cd

 

a , b     -  bases

c black   - lateral side = height

d black  - lateral side

alpha orange  -  angle  at the base

 

Calculate the base of a trapezoid if given lateral sides, angle at the base and other base  ( a b  ) :

length bases rectangular trapezoid cd Fa1  length bases rectangular trapezoid cd Fa2

length bases rectangular trapezoid cd Fb1  length bases rectangular trapezoid cd Fb2

length bases rectangular trapezoid cd F3

length bases rectangular trapezoid cd F4

 

 

3.  Sides (bases) of a right trapezoid if you know diagonals, lateral side (height) and angle between the diagonals  

length bases rectangular trapezoid d

 

a , b     -  bases

c black   - lateral side = height

d1 blue , d2 blue     -  diagonals

alpha orange , beta brown     -  angles between the diagonals

 

Calculate the side (base) of a trapezoid if given diagonals, lateral side (height) and angle between the diagonals ( a b  ) :

length bases rectangular trapezoid d F1

length bases rectangular trapezoid d F2

* It is true in this case:

length bases rectangular trapezoid d F3

 

 

4.  Sides (bases) of a right trapezoid if you know area of a trapezoid, lateral side (height) and other base  

length bases rectangular trapezoid S

 

a , b     -  bases

c black   - lateral side = height

h    -  height

A18 black    -  area

 

Calculate the side (base) of a trapezoid if given area of a trapezoid, lateral side (height) and other base ( a b  ) :

length bases rectangular trapezoid S F1    length bases rectangular trapezoid S F2

* It is true in this case:

length bases rectangular trapezoid S F3