### Theory:

Area of a Trapezium:

Formula:   Average width × Altitude (height)

Area formula:

Area =

Where $$b1, b2$$are the lengths of each base and $$h$$ is the altitude (height)

Important!
Bases are the two parallel sides of the Trapezium. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases.

Finding the height, given the area:
How to find the height (altitude) of a Trapezium give the two bases and the area. The main area formula above has four variables (area, two bases and height). If we know any three, we can always find the fourth simply by re-arranging the main formula.
Height (altitude) = $\frac{2a}{\left(\mathrm{b1}+\mathrm{b2}\right)}$
Where $$a$$ is the area and $$b1$$, $$b2$$ are the two bases.
Finding a base from the area:
How to find a base of a Trapezium give one of the bases, the height, and the area. We can find the missing base, simply by re-arranging the main formula.
Base length = $\frac{2a\phantom{\rule{0.147em}{0ex}}}{h}-b$
Where $$a$$ is the area and $$b$$ is the known base, and $$h$$ is the height (altitude).
Median:
The median(m) of a Trapezium is the line segment linking the midpoints of the non-parallel sides. Recall also that the median's length is the average of the two parallel sides.
Area = $$mh$$
Where $$m$$ is the median and $$h$$ is the height (altitude).