Right Trapezoid

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • right trapezoid 6Right trapezoid (a two-dimensional figure) is a trapezoid with only one pair of parallel edges and two adjacent right angles.
  • Acute angle is an angle that measures less than 90°.
  • Obtuse angle is an angle that measures more than 90°.
  • a & c are bases
  • b & d are legs
  • a ∥ c
  • a ≠ c
  • b ≠ d
  • ∠A < 90°
  • ∠B > 90°
  • ∠C = ∠D
  • ∠A + ∠B = 180°
  • ∠C + ∠D = 180°

Angle of a Right Trapezoid Formula

\(\large{  x = 90° - arccos \;  \frac{ d^2 + b^2 - \left(a-c \right)^2 }{ 2\;d\;b }  }\)

\(\large{  y =  180° - x }\)

Where:

\(\large{ x }\) = acute angle

\(\large{ y }\) = obtuse angle

\(\large{ a, b, c, d }\) = edge

Area of a Right Trapezoid formula

\(\large{  A_{area} = \frac{1}{2} \; d \; \left( a + c \right)   }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ a, b, c, d }\) = edge

Diagonal of a Trapezoid Formula

\(\large{  d' =  \sqrt{c^2+d^2}   }\)

\(\large{  D' = \sqrt{a^2+d^2}   }\)

Where:

\(\large{ d', D' }\) = diagonal

\(\large{ a, b, c, d }\) = edge

Midline of a Right Trapezoid formula

\(\large{  m = \frac{a+c}{2}   }\)

Where:

\(\large{ m }\) = midline

\(\large{ a, b, c, d }\) = edge

Perimeter of a Trapezoid formula

\(\large{  P =  a + b + c + d   }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ a, b, c, d }\) = edge

Side of a Right Trapezoid Formula

\(\large{  b = \sqrt{ \left( a-c \right)^2 + d^2  }  }\)

\(\large{  d = \sqrt{ b^2 - \left( a-c \right)^2  }  }\)

Where:

\(\large{ b, d }\) = edge

\(\large{ a, c }\) = edge