Trapezium area

Theorem

The area of ​​the trapezoid is equal to the half-sum of its bases and the height



Evidence



Let ABCD be a trapezoid.
The diagonal of the AC trapezoid divides it into two triangles: ABC and CDA. Consequently, the area of ​​a trapezoid is equal to the sum of the areas of these triangles.
The area of ​​the ACD triangle is



The area of ​​the triangle ABC is equal to



The heights AF and CE of these triangles are equal to the distance h between the parallel lines BC and AD, i.e. height of the trapezoid. Consequently,



The theorem is proved.