Understanding Trapezoids
A trapezoid (or trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. Trapezoids are among the most commonly encountered quadrilaterals in mathematics and everyday life.
Key Trapezoid Formulas
Area
Half the sum of the parallel sides times the height.
A = 1/2 (a + b) x h
Perimeter
Sum of all four sides.
P = a + b + c + d
Midsegment
Average of the two parallel sides.
m = (a + b) / 2
Diagonals
Computed using side lengths and height via the coordinate method.
Coordinate geometry approach
Types of Trapezoids
- Isosceles trapezoid: The non-parallel sides (legs) are equal in length. Base angles are equal.
- Right trapezoid: One leg is perpendicular to the bases, forming two right angles.
- Scalene trapezoid: No sides are equal in length.
Properties
- The sum of all interior angles is 360 degrees.
- Co-interior angles (between a base and a leg) are supplementary (sum to 180 degrees).
- The midsegment is parallel to both bases and equals their average.
- The area can also be written as A = midsegment x height.