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All basic formulas for trapezoid

Side of an isosceles trapezoid 

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

sides isosceles trapezoid m

 

a , b     -  bases

m red  - midline

 

 

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

sides isosceles trapezoid m F2sides isosceles trapezoid m F1

 

 

2.  All four sides of an isosceles trapezoid if you know height, angle at the base and other sides  

sides isosceles trapezoid h

b black   - smaller base

a  - larger base

c black    -  leg

alpha red   -  angle  at the base

h  - height

 

Calculate the lateral side (leg) of a trapezoid if given angle at the base, height or bases  ( c  ) :

sides isosceles trapezoid h F1sides isosceles trapezoid h F2

 

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

sides isosceles trapezoid h F3

sides isosceles trapezoid h F4

 

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

sides isosceles trapezoid h F5

sides isosceles trapezoid h F6

 

 

3.  Bases of an isosceles trapezoid if you know height, diagonals and angle between the diagonals  

sides isosceles trapezoid d

b black   - smaller base

a  - larger base

c black    -  leg

d blue1   -  diagonal

alpha orange , beta brown     -  angles between the diagonals

h  - height

 

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

sides isosceles trapezoid d F1sides isosceles trapezoid d F2

 

Calculate the lateral side (leg) of a trapezoid if given diagonal and bases ( c  ) :

sides isosceles trapezoid d F3

 

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

sides isosceles trapezoid d F4

sides isosceles trapezoid d F5

* It is true in this case:

sides isosceles trapezoid d F6

 

 

4.  Sides of an isosceles trapezoid if you know area of a trapezoid  

sides isosceles trapezoid S

a , b     -  bases

c black    -  leg

m12 red   -  midline

alpha orange , beta brown     -  angles at the base

h  - height

A18 black  - area

 

Calculate the side (base) of a trapezoid if given area of a trapezoid ( a b  ) :

sides isosceles trapezoid S F1sides isosceles trapezoid S F2

 

Calculate the lateral side (leg) of a trapezoid if given area of a trapezoid ( c  ) :

sides isosceles trapezoid S F3

sides isosceles trapezoid S F4

* It is true in this case:

sides isosceles trapezoid d F6

 

 

Lateral sides and height of a right trapezoid 

1.  Lateral side (height) of a right trapezoid if you know bases, other lateral side and angle at the base  

c lateral side rectangular trapezoid ab

a , b   -  bases

c black   - lateral side = height

d black  - lateral side

alpha orange  -  angle

h    -  height

 

Calculate the lateral side (height) of a trapezoid if given bases, other lateral side and angle at the base  ( c black ) :

c lateral side rectangular trapezoid ab F1

c lateral side rectangular trapezoid ab F2

c lateral side rectangular trapezoid ab F3

c lateral side rectangular trapezoid ab F4

 

 

2.  Lateral side (height) of a right trapezoid if you know diagonals, bases and angle between the diagonals  

c lateral side 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 lateral side (height) of a trapezoid if given diagonals, bases and angle between the diagonals  ( c black ) :

c lateral side rectangular trapezoid d F1

* It is true in this case:

c lateral side rectangular trapezoid d F2

 

 

3.  Lateral side (height) of a right trapezoid if you know bases or midline and area of a trapezoid   

c lateral side rectangular trapezoid S

 

a , b     -  bases

c black   - lateral side = height

m12 red  - midline

A18 black    -  area of a trapezoid

 

Calculate the lateral side (height) of trapezoid if given bases or midline and area of a trapezoid  ( c black ) :

c lateral side rectangular trapezoid S F1   c lateral side rectangular trapezoid S F2

 

 

4.  Lateral side of a right trapezoid if you know bases, other lateral side (height) and angle at the base  

c lateral side rectangular trapezoid ab

a black  - larger base

b black  - smaller base

c black   - lateral side = height

d black  - lateral side

alpha orange  -  angle  at the base

h    -  height

Calculate the lateral side of a trapezoid if given bases and lateral side(height) :( d black ) :

d lateral side rectangular trapezoid abc F1

 

Calculate the lateral side of a trapezoid if given angle at the base and bases or lateral side (height) ( d black ) :

d lateral side rectangular trapezoid abc F21   d lateral side rectangular trapezoid abc F22

 

 

5.  Lateral side of a right trapezoid if you know area of a trapezoid, angle at the base and bases or midline   

d lateral side rectangular trapezoid S

a , b     -  bases

d black   - lateral side (leg)

alpha orange  -  angle  at the base

m12 red  - midline

A18 black    -  area

 

Calculate the lateral side of trapezoid if given area of a trapezoid, angle at the base and bases or midline  ( d black ) :

d lateral side rectangular trapezoid S F1   d lateral side rectangular trapezoid S F2

 

 

Diagonal of a right trapezoid

Diagonal rectangular trapezoid

 

a , b     -  bases

c black = h     - lateral side = height

d1 blue , d2 blue     -  diagonals

 

Find the diagonals of a trapezoid if given lateral sides (height) and base, using The Pythagorean Theorem (  ) :

Diagonal rectangular trapezoid F1

Diagonal rectangular trapezoid F2

Other formulas for diagonals as for a scalene trapezoid

 

 

Midline of a right trapezoid 

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

middle line rectangular trapezoid ab

 

a , b     -  bases

m12 red  - midline

 

 

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

middle line rectangular trapezoid ab F

 

 

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

middle line rectangular trapezoid h

a black  - larger base

b black  - smaller base

d black  - lateral side

c black = h     - lateral side = height

alpha orange   -  angle at the base

m12 red  - midline

 

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

middle line rectangular trapezoid h F11  middle line rectangular trapezoid h F12

 

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

middle line rectangular trapezoid h F21  middle line rectangular trapezoid h F22

 

Find the median of a trapezoid if given base and lateral sides ( m red ) :

middle line rectangular trapezoid h F31  middle line rectangular trapezoid h F32

 

 

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

middle line rectangular 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 rectangular trapezoid d F

 

 

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

middle line rectangular 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 rectangular trapezoid S F