It is Geometry, not algebra
Formula given by both suttoncoldfield and Guest55 is of course correct.
Here is a derivation of the formula for trapezium's area.
Let us say we have a trapezium with two parallel sides (of lengths 'a' and 'b'), and a height of 'H'.
Draw a diagonal across the trapezium i.e. draw a line connecting two opposite vertices. Now, the trapezium looks like a combination of Two Triangles whose base lines are parallel to each other. These triangles have base lengths of 'a' and 'b', and both have the the same height of 'H'.
Area of Trapezium is therefore = Sum of Areas of the Two Triangles
= (aH)/2 + (bH)/2
= (a+b)H / 2
Derivation of Triangle's Area ( 1/2 x base x height) is of course a different story
Btw, I just noted this in wikipedia
The word trapezium has several meanings:
(Outside the US) – a quadrilateral with one pair of parallel sides (a shape known in the US as a trapezoid).
(In the US) – a quadrilateral with no parallel sides (a shape known elsewhere as a general irregular quadrilateral).
Didn't know that a trapezium does not have parallel sides if it is on the other side of the pond. One learns something everyday