Geometry Course/Polygon/Quadrilateral/Trapezoid

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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.

 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