Isosceles trapezoid (a two-dimensional figure) is a trapezoid with only one pair of parallel edges and having base angles that are the same.- Acute angle measures less than 90°.
- Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
- Diagonal is a line from one vertices to another that is non adjacent.
- Obtuse angle measures more than 90°.
- a & c are bases
- b & d are legs
- a ∥ c
- a ≠ c
- b = d
- ∠A & ∠D < 90°
- ∠B & ∠C > 90°
- ∠A = ∠D
- ∠B = ∠C
- ∠A + ∠B = 180°
- ∠C + ∠D = 180°
- ∠A + ∠C = 180°
- ∠B + ∠D = 180°
- 2 diagonals
- 4 edges
- 4 vertexs
- See Article Links - Geometric Properties of Structural Shapes
Angle of a Isosceles Trapezoid formulas |
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\( x \;=\; arccos \left( \dfrac{ \left( \dfrac{ a - c }{ 2 } \right)^2 + b^2 - h^2}{2 \cdot \left( \dfrac{ a - c}{2}\right) \cdot b } \right)\) \( y \;=\; 180° - x \) |
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| Symbol | English | Metric |
| \( x \) = acute angle | \( deg \) | \( deg \) |
| \( y \) = obtuse angle | \( deg \) | \( deg \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Area of an Isosceles Trapezoid formulas |
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\( A_{area} \;=\; \dfrac{h}{2} \cdot \left( c + a \right) \) \( A_{area} \;=\; h \left( \dfrac{ c + a }{ 2 } \right) \) \( A_{area} \;=\; mc \cdot sin( x) \) \( A_{area} \;=\; mc \cdot sin( y) \) |
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| Symbol | English | Metric |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( m \) = central median | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Circumcircle of an Isosceles Trapezoid formulas |
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\( R \;=\; \dfrac{ b \cdot D' \cdot c }{ 4 \cdot \sqrt{ s \cdot \left( s - b \right) \cdot \left( s - D' \right) \cdot \left( s - c \right) } } \) \( s \;=\; \dfrac{ b + D' + c }{ 2 } \) \( R \;=\; \dfrac{ b \cdot D' \cdot a }{ 4 \cdot \sqrt{ s \cdot \left( s - b \right) \cdot \left( s - D' \right) \cdot \left( s - a \right) } } \) \( s \;=\; \dfrac{ b + D' + a }{ 2 } \) \( R \;=\; b \cdot \sqrt{ \dfrac{ a \cdot c + b^2 }{ 4 \cdot b^2 - \left( a - c \right)^2} } \) |
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| Symbol | English | Metric |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Diagonal of an Isosceles Trapezoid formula |
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| \( D' \;=\; \sqrt { b^2 + c \cdot a } \) | ||
| Symbol | English | Metric |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Distance from Centroid of an Isosceles Trapezoid formulas |
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\( C_x \;=\; \dfrac{ a }{ 2 } \) \( C_y \;=\; \dfrac{ h }{ 3} \cdot \left( \dfrac{ 2 \cdot c + a }{ c + a } \right) \) |
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| Symbol | English | Metric |
| \( C \) = distance from centroid | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Elastic Section Modulus of an Isosceles Trapezoid formulas |
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\( S_x \;=\; \dfrac{ I_x }{ C_y } \) \( S_y \;=\; \dfrac{ I_y }{ C_x } \) |
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| Symbol | English | Metric |
| \( S \) = elastic section modulus | \( in^3\) | \( mm^3 \) |
| \( C \) = distance from centroid | \( in \) | \( mm \) |
| \( I \) = moment of inertia | \(lbm \;/\; ft^2-sec\) | \(kg \;/\; m^2\) |
Height of an Isosceles Trapezoid formula |
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| \( h \;=\; \dfrac{1}{2} \cdot \sqrt { 4 \cdot b^3 - {c + a} } \) | ||
| Symbol | English | Metric |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Perimeter of an Isosceles Trapezoid formulas |
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\( P \;=\; 2 \cdot b + c + a \) \( P \;=\; 2 \cdot \sqrt{ h^2 + \dfrac{ \left( b - a \right)^2 }{ 4 } } + a + b \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Plastic Section Modulus of an Isosceles Trapezoid formulas |
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\( Z_x \;=\; \dfrac{ h \cdot \left( 2 \cdot c^2 - c\;a + 2 \cdot a^2 \right) }{ 12 } \) \( Z_y \;=\; \dfrac{ h^2 \cdot \left( 11 \cdot c^2 + 26 \cdot c \cdot a + 11 \cdot a^2 \right) }{ 48 \cdot \left( c + a \right) } \) |
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| Symbol | English | Metric |
| \( Z \) = plastic section modulus | \( in^3 \) | \( mm^3 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Polar Moment of Inertia of an Isosceles Trapezoid formulas |
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\( J_{z} \;=\; I_x + I_y \) \( J_{z1} \;=\; I_{x1} + I_{y1} \) |
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| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
Radius of Gyration of an Isosceles Trapezoid formulas |
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\( k_{x} \;=\; \dfrac{ h }{ 6 } \cdot \sqrt{ 2 + \dfrac{ 4 \cdot c \cdot a }{ \left( c + a \right)^2 } } \) \( k_{y} \;=\; \dfrac{ 1 }{ 12 } \cdot \sqrt{ 6 \left( c^2 + a^2 \right) } \) \( k_{z} \;=\; \sqrt{ k_{x}{^2} + k_{y}{^2} } \) \( k_{y1} \;=\; \sqrt{ \dfrac{ 3 \cdot a + 5 \cdot c }{ 12 \cdot \left( a + c \right) } \cdot a } \) \( k_{z1} \;=\; \sqrt{ k_{x1}{^2} + k_{y1}{^2} } \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Second Moment of Area of an Isosceles Trapezoid formulas |
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\( I_{x} =\;=\; \dfrac{ h^3 \cdot \left( c^2 + 4 \cdot c \cdot a + a^2 \right) }{ 36 \cdot \left( c + a \right) } \) \( I_{y} \;=\; \dfrac{ h \cdot \left( c + a \right) \cdot \left( c^2 + a^2 \right) }{ 48 } \) \( I_{x1} \;=\; \dfrac{ h^3 \cdot \left( 3 \cdot c + a \right) }{ 12 } \) \( I_{y1} \;=\; \dfrac{ h \cdot \left( c + a \right) \cdot \left( c^2 + 7 \cdot a^2 \right) }{ 48 } \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
