1.  How to find the area of a trapezoid (called a trapezium in the UK) if you know bases, height and middle line of a trapezoid  

area of trapezoid m

 

a , b     -  bases

h  - height

m red - middle line

A-black  -  area of a trapezoid

 

Formula for area of a trapezoid if given bases, height and middle line. As well as you can use the calculator for calculating area. ( A ) :

area of trapezoid m formula1

area of trapezoid m formula2

 

 

2.  How to find the area of a trapezoid (trapezium UK) if you know diagonals and angle between them

area of trapezoid d

 

d1 blue , d2 blue -  diagonals

alpha red , beta green -  angles between the diagonals

A-black  -  area of a trapezoid

 

Formula for area of a trapezoid if given diagonals and angle between them. As well as you can use the calculator for calculating area ( A ) :

area of trapezoid d formula1  area of trapezoid d formula2

 

 

3.  How to find the area of a trapezoid (trapezium UK) if you know all sides  

area of trapezoid side

 

 

a , b , c , d black   -  sides

A-black  -  area of a trapezoid

 

Formula for area of a trapezoid if given all four sides. As well as you can use the calculator for calculating area ( A ) :

area of trapezoid side formula

 

 

Definition of a trapezoid (also known as trapezium)  

Trapezoid is a quadrilateral in which only one pair of opposite sides are parallel

 

Properties of a trapezoid (trapezium UK)  

1. The middle line of the trapezoid is parallel to the bases and is equal to their half-sum.

2. The bisector of any angle of the trapezoid cuts off on its base (or continuation) an interval equal to the leg.

3. The triangles , formed by segments of the diagonals and the bases of the trapezoid, are similar.

4. Triangles formed by segments of the diagonals and the leg of the trapezoid, have the same area.

5. A circle can be inscribed into a trapezoid if the sum of the bases of the trapezoid is equal to the sum of its lateral sides.

6. The segment connecting the midpoints of the diagonals is equal to the half-difference of the bases and lies on the midline.

7. The intersection point of the diagonals of the trapezoid, the point of intersection of the extensions of its lateral sides and the middle of the bases lie on one straight line.

8. If the sum of the angles at any base of the trapezoid is 90 °, then the segment connecting the midpoints of the bases is equal to their half-difference.