Parallelogram (a two-dimensional figure) is a quadrilateral with two pairs of parallel opposite sides.- Acute angle measures less than 90°.
- Diagonal is a line from one vertices to another that is non adjacent.
- Obtuse angle measures more than 90°.
- Opposite sides are congurent and parallel.
- Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
- Quadrilateral (a two-dimensional figure) is a polygon with four sides.
- a ∥ c
- b ∥ d
- ∠A & ∠C < 90°
- ∠B & ∠D > 90°
- ∠A + ∠B = 180°
- ∠C + ∠D = 180°
- 2 diagonals
- 4 edges
- 4 vertexs
Angle of a Parallelogram formulas |
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\( cos( x) \;=\; \dfrac{ a^2 + b^2 - d'^2 }{ 2 \cdot a \cdot b } \) \( cos( y) \;=\; \dfrac{ a^2 + b^2 - D'^2 }{ 2 \cdot a \cdot b } \) \( sin( x) \;=\; sin( y) \cdot \dfrac{A }{ a \cdot b } \) |
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| Symbol | English | Metric |
| \( x \) = acute angles | \( deg\) | \( rad\) |
| \( y \) = obtuce angles | \( deg\) | \( rad\) |
| \( d', D' \) = diagonal | \( in\) | \( mm \) |
| \( a, b, c, d \) = edge | \( in\) | \( mm \) |
| \( A, B, C, D \) = vertex | \( in\) | \( mm \) |
Area of a Parallelogram formulas |
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\( A_{area} \;=\; a\cdot h_a \) \( A_{area} \;=\; b\cdot h_b \) \( A_{area} \;=\; a\cdot b \cdot sin( x) \) \( A_{area} \;=\; a\cdot b \cdot sin( y) \) |
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| Symbol | English | Metric |
| \( A_{area} \) = area | \( in^2\) | \( mm^2 \) |
| \( a, b, c, d \) = edge | \( in\) | \( mm \) |
| \( h_a, h_b \) = height | \( in\) | \( mm \) |
Diagonal of a Parallelogram formulas |
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\( d' \;=\; \sqrt{ a^2 \cdot b^2 - 2\cdot a\cdot b \cdot cos( x ) } \) \( d' \;=\; \sqrt{ a^2 + b^2 + 2\cdot a\cdot b \cdot cos( y) } \) \( D' \;=\; \sqrt{ a^2 + b^2 - 2\cdot a\cdot b \cdot cos( y) } \) \( D' \;=\; \sqrt{ a^2 + b^2 + 2\cdot a\cdot b \cdot cos( x) } \) \( d' \;=\; \sqrt{ 2\cdot a^2 + 2\cdot b^2 - D'^2 } \) \( D' \;=\; \sqrt{ 2\cdot a^2 + 2\cdot b^2 - d'^2 } \) |
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| Symbol | English | Metric |
| \( d', D' \) = diagonal | \( in\) | \( mm \) |
| \( x \) = acute angles | \( deg\) | \( rad\) |
| \( a, b, c, d \) = edge | \( in\) | \( mm \) |
| \( y \) = obtuce angles | \( deg\) | \( rad\) |
Edge of a Parallelogram formulas |
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\( a \;=\; \dfrac{P}{2} - b \) \( b \;=\; \dfrac{P}{2} - a \) \( b \;=\; \dfrac{A}{h} \) \( a \;=\; \dfrac{h_b}{sin( x) } \) \( a \;=\; \dfrac{h_b}{sin( y) } \) \( b \;=\; \dfrac{h_a}{sin( x) } \) \( b \;=\; \dfrac{h_a}{sin( y) } \) \( a \;=\; \sqrt{ \dfrac{D'^2 + d'^2 - 2\cdot b^2 }{2} } \) \( b \;=\; \sqrt{ \dfrac{D'^2 + d'^2 - 2\cdot a^2 }{2} } \) |
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| Symbol | English | Metric |
| \( a, b, c, d \) = edge | \( in\) | \( mm \) |
| \( x \) = acute angles | \( deg\) | \( rad\) |
| \( d', D' \) = diagonal | \( in\) | \( mm \) |
| \( h_a, h_b \) = height | \( in\) | \( mm \) |
| \( y \) = obtuce angles | \( deg\) | \( rad\) |
| \( P \) = perimeter | \( in\) | \( mm \) |
Height of a Parallelogram formulas |
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\( h_a \;=\; \dfrac {A}{b} \) \( h_a \;=\; b \cdot sin( x) \) \( h_a \;=\; b \cdot sin( y) \) \( h_b \;=\; a \cdot sin( x) \) \( h_b \;=\; a \cdot sin( y) \) |
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| Symbol | English | Metric |
| \( h_a, h_b \) = height | \( in\) | \( mm \) |
| \( x \) = acute angles | \( deg\) | \( rad\) |
| \( A_{area} \) = area | \( in^2\) | \( mm^2 \) |
| \( a, b, c, d \) = edge | \( in\) | \( mm \) |
| \( y \) = obtuce angles | \( deg\) | \( rad\) |
Perimeter of a Parallelogram formulas |
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\( P \;=\; 2 \cdot \left( a + b \right) \) \( P \;=\; 2\cdot a + 2\cdot b \) \( P \;=\; 2\cdot a + \sqrt{ D'^2 + d'^2 - 4\cdot a^2 } \) \( P \;=\; 2\cdot b + \sqrt{ D'^2 + d'^2 - 4\cdot b^2 } \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in\) | \( mm \) |
| \( d', D' \) = diagonal | \( in\) | \( mm \) |
| \( a, b, c, d \) = edge | \( in\) | \( mm \) |
