Kite

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

Kite Index

 

Angle of a Kite formulas

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

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

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

Symbol English Metric
\(\large{ x }\) = acute angle \(\large{ deg }\) \(\large{ rad }\)
\(\large{ y }\) = obtuse angle \(\large{ deg }\) \(\large{ rad }\)
\(\large{ z }\) = acute angle \(\large{ deg }\) \(\large{ rad }\)
\(\large{ d' }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ D' }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ m }\) = diagonal section \(\large{ in }\) \(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

Area of a Kite formulas

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

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

Symbol English Metric
\(\large{ A_{area} }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ d' }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ D' }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ m, n, r, v }\) = diagonal \(\large{ in }\) \(\large{ mm }\)

  

Diagonal of a Kite formulas

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

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

Symbol English Metric
\(\large{ d' }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ D' }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ A_{area} }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)

    

Edge of a Kite formulas

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

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

Symbol English Metric
\(\large{ a, b, c, d }\) = edge \(\large{ in }\) \(\large{ mm }\)
\(\large{ p }\) = perimeter \(\large{ in }\) \(\large{ mm }\)

 

Perimeter of a Kite formulas

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

\(\large{ p= 2\;a + 2\;c }\) 

Symbol English Metric
\(\large{ p }\) = perimeter \(\large{ in }\) \(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Quadrilateral