Rhombus
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
Angle of a Rhombus formula
\(\large{ y = 180° - x }\) |
Where:
\(\large{ x }\) = acute angle
\(\large{ y }\) = obtuse angle
Area of a Rhombus formulas
\(\large{ A_{area} = \frac {D' \;d' } {2} }\) | |
\(\large{ A_{area} = h \;a }\) | |
\(\large{ A_{area} = a^2 \; sin\; x }\) | |
\(\large{ A_{area} = 2\; a\; r }\) | |
\(\large{ A_{area} = \frac{4\; r^2}{sin\;x} }\) |
Where:
\(\large{ A_{area} }\) = area
\(\large{ d', D' }\) = diagonal
\(\large{ a, b, c, d }\) = edge
\(\large{ r }\) = inside radius
\(\large{ x }\) = acute angle
\(\large{ y }\) = obtuse angle
Angle of a Rhombus formulas
\(\large{ sin \; x = \frac {2\;D'\;d'}{D'^2 \;+\; d'^2} }\) | |
\(\large{ sin \; y = \frac {2\;D'\;d'}{D'^2 \;+\; d'^2} }\) | |
\(\large{ cos \; x = 1 - \frac {d'^2}{2\; a^2} }\) | |
\(\large{ cos \; x = \frac {D'^2}{2\; a^2} - 1 }\) | |
\(\large{ cos \; y = 1 - \frac {D'^2}{2\; a^2} }\) | |
\(\large{ cos \; y = \frac {d'^2}{2\; a^2} - 1 }\) | |
\(\large{ sin \; x = \frac {A}{a^2 } }\) | |
\(\large{ sin \; y = \frac {A}{a^2 } }\) |
Where:
\(\large{ x }\) = acute angle
\(\large{ y }\) = obtuse angle
\(\large{ A_{area} }\) = area
\(\large{ d',\; D' }\) = diagonal
\(\large{ a, b, c, d }\) = edge
Diagonal of a Rhombus formulas
\(\large{ d' = \frac {2\;A_{area}}{D'} }\) | |
\(\large{ D' = \frac {2\;A_{area}}{d'} }\) | |
\(\large{ d' = \sqrt{ 4\;a^2 - D'^2 } }\) | |
\(\large{ D' = \sqrt{ 4\;a^2 - d'^2 } }\) | |
\(\large{ d' = a \sqrt{ 2 - 2 \; cos \; x } }\) | |
\(\large{ d' = a \sqrt{ 2+ 2 \; cos \; y } }\) | |
\(\large{ D' = a \sqrt{ 2 - 2 \; cos \; y } }\) | |
\(\large{ D' = a \sqrt{ 2 + 2 \; cos \; x } }\) | |
\(\large{ d' = 2\;a \; cos \left( \frac{y}{ 2} \right) }\) | |
\(\large{ d' = 2\;a \; sin \left( \frac{x}{ 2} \right) }\) | |
\(\large{ D' = 2\;a \; cos \left( \frac{x}{ 2} \right) }\) | |
\(\large{ D' = 2\;a \; sin \left( \frac{y}{ 2} \right) }\) |
Where:
\(\large{ d', D' }\) = diagonal
\(\large{ A_{area} }\) = area
\(\large{ a, b, c, d }\) = edge
\(\large{ x }\) = acute angle
\(\large{ y }\) = obtuse angle
Edge of a Rhombus formulas
\(\large{ a = \frac {P} {4} }\) | |
\(\large{ a = \frac { \sqrt { {D'}^2 \;+\; {D'}^2 } } { 2 } }\) | |
\(\large{ a = \sqrt{ \frac{ A }{ sin\;x } } }\) | |
\(\large{ a = \sqrt{ \frac{ A }{ sin\;y } } }\) | |
\(\large{ a = \frac {d'} { \sqrt{ 2 \;-\; 2 \; cos\; x } } }\) | |
\(\large{ a = \frac {d'} { \sqrt{ 2 \;+\; 2 \; cos\; y } } }\) | |
\(\large{ a = \frac {D'} { \sqrt{ 2 \;-\; 2 \; cos\; y } } }\) | |
\(\large{ a = \frac {D'} { \sqrt{ 2 \;+\; 2 \; cos\; x } } }\) | |
\(\large{ a = \sqrt{ \frac{ D' \; d' }{ 2 \; sin \; x } } }\) | |
\(\large{ a = \sqrt{ \frac{ D' \; d' }{ 2 \; sin \; y } } }\) |
Where:
\(\large{ a, b, c, d }\) = edge
\(\large{ A_{area} }\) = area
\(\large{ d',\; D' }\) = diagonal
\(\large{ P }\) = perimeter
\(\large{ x }\) = acute angle
\(\large{ y }\) = obtuse angle
Inscribed Circle Radius of a Rhombus formulas
\(\large{ r = \frac{h}{2} }\) | |
\(\large{ r = \frac{A_{area}}{2 a} }\) | |
\(\large{ r = \frac{D' \; d'}{4 a} }\) | |
\(\large{ r = \frac{ \sqrt{A_{area}\;sin\;x } }{2} }\) | |
\(\large{ r = \frac{a\;sin\;x}{2} }\) | |
\(\large{ r = \frac{a\;sin\;y}{2} }\) | |
\(\large{ r = \frac{ D'\;sin \frac{x}{2} }{2} }\) | |
\(\large{ r = \frac{ d'\;sin \frac{y}{2} }{2} }\) | |
\(\large{ r = \frac{ D'\; d' }{ 2\;\sqrt{ D'^2 \;+\; d'^2 } } }\) |
Where:
\(\large{ r }\) = inside radius
\(\large{ A_{area} }\) = area
\(\large{ d',\; D' }\) = diagonal
\(\large{ h }\) = hight
\(\large{ a, b, c, d }\) = edge
Perimeter of a Rhombus formulas
\(\large{ P = 4\;a }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ a, b, c, d }\) = edge