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