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 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.
Recall though that the median is half of the sum of the bases.
Substituting for m, we get: