# 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° 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 b$_1$ and b$_2$).
* 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:
    $A={\frac {1}{2}}(b_{1}+b_{2})h$

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