1. To find the missing base length of a trapezoid (called a trapezium in the UK) if you know other base and midsegment  

sides trapezoid m

 

a , b     -  bases of a trapezoid

m red  - middle line

 

 

Formulas for trapezoid base. Click on the formula image to use the calculator.

sides trapezoid m F asides trapezoid m F b

 

 

2.  To find the legs and bases of a trapezoid (trapezium UK) with height, angle and other sides  

sides trapezoid h

 

a , b     -  bases

c black , d black     -  legs of a trapezoid

alpha red , beta2 blue     -  angles  at the base

h  - height

 

Formulas for trapezoid base if given height, base angle and other base

sides trapezoid h F1

sides trapezoid h F2

 

Formulas for trapezoid base if given leg, base angle and other base

sides trapezoid F12

sides trapezoid F13

sides trapezoid F14

sides trapezoid F15

 

Formulas for trapezoid legs if given base angles and other leg

sides trapezoid F10sides trapezoid F11

 

 

Formulas for trapezoid legs if given base angles and height

sides trapezoid h F5sides trapezoid h F6

 

 

3.  To find bases of a trapezoid (trapezium UK) with height, diagonals and angle between them  

sides trapezoid d

 

a , b     -  bases

d1 blue , d2 blue     -  diagonals

alpha red , beta brown     -  angles between the diagonals

h  - height

 

Formulas for calculating trapezoid base if given height, diagonals and angle between them

sides trapezoid d F1

sides trapezoid d F2

* It is true in this case:

sides trapezoid d F



 

 


1.  Diagonals of a trapezoid if you know sides and angles at the base  

diagonals trapezoid abcd

a , b     -  bases

c black , d black     -  legs

alpha orange , beta brown     -  angles  at the base

d1 blue , d2 blue     -  diagonals

 

Find the diagonal of a trapezoid using the law of cosines  (  ) :

diagonals trapezoid abcd F1

diagonals trapezoid abcd F2

 

Find the diagonal of a trapezoid if given all four sides  (  ) :

diagonals trapezoid abcd F3

diagonals trapezoid abcd F4

 

 

2.  Diagonals of a trapezoid using height  

diagonals trapezoid h

a , b     -  bases

c black , d black     -  legs

alpha orange , beta brown     -  angles  at the base

d1 blue , d2 blue     -  diagonals

h  - height

 

Find the diagonal of a trapezoid using height, angles at the base and sides  ( d1d2 ) :

diagonals trapezoid h F1

diagonals trapezoid h F2

diagonals trapezoid h F3

 

diagonals trapezoid h F4

diagonals trapezoid h F5

diagonals trapezoid h F6

 

 

3.  Diagonals of a trapezoid if you know other diagonal, angle between the diagonals and height or area or midsegment  

diagonals trapezoid m

a , b     -  bases

d1 blue , d2 blue     -  diagonals

alpha orange , beta brown     -  angles between the diagonals

h  - height

m12 red  - midsegment

A18 black  - areaof a trapezoid

 

Find the diagonal of a trapezoid if given other diagonal, angle between the diagonals and height or area or midsegment  (  ) :

 

diagonals trapezoid m F11    diagonals trapezoid m F21

diagonals trapezoid m F12    diagonals trapezoid m F22

diagonals trapezoid m F13    diagonals trapezoid m F23

* It is true in this case:

diagonals trapezoid m F3

 

 

4.  Diagonals of a trapezoid using formula for the sum of the squared diagonals   

diagonals trapezoid f

a black  - lower base

b black  - upper base

c black , d black     -  legs

d1 blue , d2 blue     -  diagonals

 

Formula for the sum of the squared diagonals   :

diagonals trapezoid f F1

 

Find the diagonal of a trapezoid using formula for the sum of the squared diagonals  (  ) :

diagonals trapezoid f F2

diagonals trapezoid f F3



 

 


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

middle line trapezoid

 

a , b     -  bases

m12 red  - midline

 

 

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

middle line trapezoid F

 

 

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

middle line trapezoid h

a black  - lower base

b black  - upper base

alpha orange , beta brown     -  angles 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 trapezoid h F1

middle line trapezoid h F2

 

 

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

middle line trapezoid d

 

d1 blue , d2 blue     -  diagonals

alpha orange , beta brown     -  angles between the diagonals

h  - height

m12 red  - midline

 

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

middle line trapezoid d F

* It is true in this case:

middle line trapezoid m F3

 

 

4.  Median of a trapezoid (also known as midline or midsegment), if you know height and area of a trapezoid

middle line trapezoid S

 

A18 black  - areaof a trapezoid

h  - height

m12 red  - midline

 

Find the median of a trapezoid if given height and area of a trapezoid ( m red ) :

middle line trapezoid S F



 

 


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

height trapezoid abcd

a , b   -  bases

c black , d black     -  legs (lateral side)

alpha orange , beta brown     -  angles  at the base

h  - height

 

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

height trapezoid abcd F1

 

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

height trapezoid abcd F21   height trapezoid abcd F22

 

 

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

height trapezoid d

a , b     -  bases

d1 blue , d2 blue     -  diagonals

alpha orange , beta brown   -  angles between the diagonals

m12 red  - midline

h  - height

 

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

height trapezoid d F1

 

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

height trapezoid d F2

 

 

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

height 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 trapezoid S F1   height trapezoid S F2