Kite

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • kite 3Kite (a two-dimensional figure) is a quadrilateral with two pairs of adjacent sides that are congruent.
  • Acute angle measures less than 90°.
  • Congruent is all sides having the same lengths and angles measure the same.
  • Diagonal is a line from one vertices to another that is non adjacent.
  • Obtuse angle measures more than 90°.
  • a = b
  • c = d
  • ∠B = ∠D
  • ∠A ≠ ∠C
  • ∠A + ∠B + ∠C + ∠D = 360°
  • 2 diagonals
  • 4 sides
  • 4 vertexs

Angle of a Kite Formula

\(\large{  x = arccos \;  \frac{ m^2 + a^2 - \left( \frac{d'}{2} \right)^2 }{ 2\;m\;a }  }\)

\(\large{  y =  \frac{360° - x - z}{2}    }\)

\(\large{  z = arccos \; \frac{ \left( D'\;m\right)^2 + d^2 - \left( \frac{d'}{2} \right)^2 }{ 2\;\left( D'\;m\right)\;d }  }\)

Where:

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

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

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

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

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

\(\large{ m }\) = diagonal section

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

Area of a Kite formula

\(\large{ A_{area} =\frac { {d'}  \; {D'} }{2} }\)

\(\large{ A_{area} =\frac{1}{2} \; n \; r  }\)

Where:

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

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

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

\(\large{ m, n, r, v }\) = diagonal

Diagonal of a Kite formula

\(\large{ d' = 2\; \frac {A}   {D'} }\)

\(\large{ D' = 2\; \frac {A}   {d'} }\)

Where:

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

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

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

Edge of a Kite formula

\(\large{ a = \frac {p}   {2}\; - c   }\)

\(\large{ c = \frac {p}   {2} \;- a   }\)

Where:

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

\(\large{ p }\) = perimeter

Perimeter of a Kite formula

\(\large{ p= 2\; \left( a + c   \right) }\)

\(\large{ p= 2\;a + 2\;c }\)

Where:

\(\large{ p }\) = perimeter

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