Trapezoid

Written by Jerry Ratzlaff on . Posted in Plane Geometry

 

trapezoid 2

trapezoid

  • A trapezoid has two edges (\(b\) and \(d\)) that are parallel lines.
  • The two parallel edges (\(b\) and \(d\)) are called the base of the trapezoid.
  • Trapezoid is a quadrilateral with only one pair of parallel edges.
  • Edge \(a\) and \(c\) are called legs
  • Edge \(\;a = c\)
  • Angle \(\;A = D\)
  • Angle \(\;B = C\)
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Edge formula

\(a = P-b-c-d \)

\(b = P-c-d-a \)

\(b = 2 \frac {A}{h} -d \)

\(c = P-d-a-b \)

\(d = P-a-b-c \)

\(d = 2 \frac {A}{h} -b \)

Where:

\(a\) = edge

\(b\) = edge

\(c\) = edge

\(d\) = edge

\(h\) = height

\(P\) = perimeter

\(A\) = area

Height formula

\(h = 2 \frac {A} {a+b} \)

Where:

\(h\) = height

\(a\) = edge

\(b\) = edge

\(A\) = area

Perimeter formula

\(P=a+b+c+d \)

Where:

\(P\) = perimeter

\(a\) = edge

\(b\) = edge

\(c\) = edge

\(d\) = edge

Area formula

\(A=\frac{h}{2}(b-d) \)

\(A=\frac{b+d}{2} h \)

Where:

\(A\) = area

\(b\) = edge

\(d\) = edge

\(h\) = height