Rhombus

on 29 January 2016. Posted in Plane Geometry

Rhombus (a two-dimensional figure) is a parallelogram with four congruent sides.
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.
Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
Obtuse angle measures more than 90°.
Parallelogram (a two-dimensional figure) is a quadrilateral with two pairs of parallel opposite sides.
a ∥ c
b ∥ d
a = b = c = d
∠A & ∠C < 90°
∠B & ∠D > 90°
∠A + ∠B = 180°
∠C + ∠D = 180°
4 angle
2 diagonals
4 edges
4 vertexs

Area of a Rhombus formulas
\(\large{ A_{area} = \frac {D' \;d' } {2} }\) \(\large{ A_{area} = h \;a }\) \(\large{ A_{area} = a^2 \; sin\; x }\) \(\large{ A_{area} = 2\; a\; r }\) \(\large{ A_{area} = \frac{4\; r^2}{sin\;x} }\)
Symbol	English	Metric
\(\large{ A_{area} }\) = area	\(\large{ in^2}\)	\(\large{ mm^2 }\)
\(\large{ x }\) = acute angles	\(\large{ deg}\)	\(\large{ rad}\)
\(\large{ d', D' }\) = diagonal	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ r }\) = inside radius	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ y }\) = obtuce angles	\(\large{ deg}\)	\(\large{ rad}\)

Angle of a Rhombus formulas
\(\large{ sin \; x = \frac {2\;D'\;d'}{D'^2 \;+\; d'^2} }\) \(\large{ sin \; y = \frac {2\;D'\;d'}{D'^2 \;+\; d'^2} }\) \(\large{ cos \; x = 1 - \frac {d'^2}{2\; a^2} }\) \(\large{ cos \; x = \frac {D'^2}{2\; a^2} - 1 }\) \(\large{ cos \; y = 1 - \frac {D'^2}{2\; a^2} }\) \(\large{ cos \; y = \frac {d'^2}{2\; a^2} - 1 }\) \(\large{ sin \; x = \frac {A}{a^2 } }\) \(\large{ sin \; y = \frac {A}{a^2 } }\)
Symbol	English	Metric
\(\large{ x }\) = acute angles	\(\large{ deg}\)	\(\large{ rad}\)
\(\large{ A_{area} }\) = area	\(\large{ in^2}\)	\(\large{ mm^2 }\)
\(\large{ d', D' }\) = diagonal	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ y }\) = obtuce angles	\(\large{ deg}\)	\(\large{ rad}\)

Diagonal of a Rhombus formulas
\(\large{ d' = \frac {2\;A_{area}}{D'} }\) \(\large{ D' = \frac {2\;A_{area}}{d'} }\) \(\large{ d' = \sqrt{ 4\;a^2 - D'^2 } }\) \(\large{ D' = \sqrt{ 4\;a^2 - d'^2 } }\) \(\large{ d' = a \sqrt{ 2 - 2 \; cos \; x } }\) \(\large{ d' = a \sqrt{ 2+ 2 \; cos \; y } }\) \(\large{ D' = a \sqrt{ 2 - 2 \; cos \; y } }\) \(\large{ D' = a \sqrt{ 2 + 2 \; cos \; x } }\) \(\large{ d' = 2\;a \; cos \left( \frac{y}{ 2} \right) }\) \(\large{ d' = 2\;a \; sin \left( \frac{x}{ 2} \right) }\) \(\large{ D' = 2\;a \; cos \left( \frac{x}{ 2} \right) }\) \(\large{ D' = 2\;a \; sin \left( \frac{y}{ 2} \right) }\)
Symbol	English	Metric
\(\large{ d', D' }\) = diagonal	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ x }\) = acute angles	\(\large{ deg}\)	\(\large{ rad}\)
\(\large{ A_{area} }\) = area	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ y }\) = obtuce angles	\(\large{ deg}\)	\(\large{ rad}\)

Edge of a Rhombus formulas
\(\large{ a = \frac {P} {4} }\) \(\large{ a = \frac { \sqrt { {D'}^2 \;+\; {D'}^2 } } { 2 } }\) \(\large{ a = \sqrt{ \frac{ A }{ sin\;x } } }\) \(\large{ a = \sqrt{ \frac{ A }{ sin\;y } } }\) \(\large{ a = \frac {d'} { \sqrt{ 2 \;-\; 2 \; cos\; x } } }\) \(\large{ a = \frac {d'} { \sqrt{ 2 \;+\; 2 \; cos\; y } } }\) \(\large{ a = \frac {D'} { \sqrt{ 2 \;-\; 2 \; cos\; y } } }\) \(\large{ a = \frac {D'} { \sqrt{ 2 \;+\; 2 \; cos\; x } } }\) \(\large{ a = \sqrt{ \frac{ D' \; d' }{ 2 \; sin \; x } } }\) \(\large{ a = \sqrt{ \frac{ D' \; d' }{ 2 \; sin \; y } } }\)
Symbol	English	Metric
\(\large{ a, b, c, d }\) = edge	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ x }\) = acute angles	\(\large{ deg}\)	\(\large{ rad}\)
\(\large{ A_{area} }\) = area	\(\large{ in^2}\)	\(\large{ mm^2}\)
\(\large{ d',\; D' }\) = diagonal	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ P }\) = perimeter	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ y }\) = obtuce angles	\(\large{ deg}\)	\(\large{ rad}\)

Inscribed Circle Radius of a Rhombus formulas
\(\large{ r = \frac{h}{2} }\) \(\large{ r = \frac{A_{area}}{2 a} }\) \(\large{ r = \frac{D' \; d'}{4 a} }\) \(\large{ r = \frac{ \sqrt{A_{area}\;sin\;x } }{2} }\) \(\large{ r = \frac{a\;sin\;x}{2} }\) \(\large{ r = \frac{a\;sin\;y}{2} }\) \(\large{ r = \frac{ D'\;sin \frac{x}{2} }{2} }\) \(\large{ r = \frac{ d'\;sin \frac{y}{2} }{2} }\) \(\large{ r = \frac{ D'\; d' }{ 2\;\sqrt{ D'^2 \;+\; d'^2 } } }\)
Symbol	English	Metric
\(\large{ r }\) = inside radius	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ A_{area} }\) = area	\(\large{ in^2}\)	\(\large{ mm^2}\)
\(\large{ d',\; D' }\) = diagonal	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c, d }\) = edge	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ h }\) = hight	\(\large{ in}\)	\(\large{ mm}\)

Perimeter of a Rhombus formulas
\(\large{ P = 4\;a }\)
Symbol	English	Metric
\(\large{ P }\) = perimeter	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c, d }\) = edge	\(\large{ in}\)	\(\large{ mm}\)

Piping Designer Logo 1

Angle of a Rhombus formula