Geometry/Trapezoids

A Trapezoid (American English) or Trapezium (British English) is a quadrilateral that has two parallel sides and two non parallel sides.

Some properties of trapezoids:
 * The interior angles sum to 360&deg; as in any quadrilateral.
 * The parallel sides are unequal.
 * Each of the parallel sides is called a base (b) of the trapezoid. The two angles that join one base are called 'base angles'.
 * If the two non-parallel sides are equal, the trapezoid is called an isosceles trapezoid.
 * In an isosceles trapezoid, each pair of base angles are equal.
 * If one pair of base angles of a trapezoid are equal, the trapezoid is isosceles.
 * A line segment connecting the midpoints of the non-parallel sides is called the median (m) of the trapeziod.
 * The median of a trapezoid is equal to one half the sum of the bases (called b1 and b2).
 * A line segment perpendicular to the bases is called an altitude (h) of the trapezoid.

The area (A) of a trapezoid is equal to the product of an altitude and the median.
 * $$ A = mh$$

Recall though that the median is half of the sum of the bases.
 * $$ m = \frac {1}{2}(b_1+b_2) $$

Substituting for m, we get:
 * $$ A = \frac {1}{2}(b_1+b_2) h $$