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   Trapezoid
Bases of a trapezoid: a, b
Legs of a trapezoid: c, d
Midline of a trapezoid: m
Altitude of a trapezoid: h
Perimeter: P
Diagonals of a trapezoid: p, q
Angle between the diagonals: φ
Radius of the circumscribed circle: R
Radius of the inscribed circle: r
Area: S
  1. 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.

    trapezoid

  2. 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.

  3. 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,   m||a,   m||b

  4. Diagonals of a trapezoid (if a > b)

    diagonals of a trapezoid

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

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

    area of a trapezoid

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

    isosceles trapezoid with a circumscribed circle

  8. Radius of the circle circumscribed about an isosceles trapezoid

    radius of the circumscribed circle

  9. Diagonal of an isosceles trapezoid

    diagonal of an isosceles trapezoid

  10. Altitude of an isosceles trapezoid

    altitude of an isosceles trapezoid

  11. 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

    trapezoid with an inscribed circle

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


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