
A trapezoid (or a trapezium) is a quadrilateral in which (at least) one pair of opposite sides is parallel.
Sometimes a trapezoid is defined as a quadrilateral having exactly one pair of parallel sides. The parallel sides are called
the bases, and two other sides are called the legs.

A trapezoid in which the legs are equal is called an isosceles trapezoid.
A trapezoid in which at least one angle is the right
angle (90°) is called a right trapezoid.

The midline of a trapezoid is parallel to the bases and equal to the arithmetic mean of the lengths of the bases.
m = (a + b)/2, ma, mb

Diagonals of a trapezoid (if a > b)

Perimeter of a trapezoid
P = a + b + c + d

Area of a trapezoid
S = (a + b)/2 ⋅ h = mh,

All four vertices of an isosceles trapezoid lie on a circumscribed circle.

Radius of the circle circumscribed about an isosceles trapezoid

Diagonal of an isosceles trapezoid

Altitude of an isosceles trapezoid

If the sum of the bases of a trapezoid is equal to the sum of its legs, all four sides of the trapezoid are tangents to
an inscribed circle:
a + b = c + d

Radius of the inscribed circle
r = h/2,
where h is the altitude of the trapezoid.