Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Rectangle - Geometric Properties

• Rectangle is a quadrilateral with two pair of parallel edges.
• 4 interior angles are 90°
• 2 diagonals
• 4 edges
• 4 vertexs

Area of a Rectangle formula

$$\large{ A_{area} = ab }$$

Circumcircle of a Rectangle formula

The radius of a circumcircle (outer) of a square if given side of diagonal $$( R )$$.

$$\large{ R = \frac {D'}{2} }$$

$$\large{ R = \frac { \sqrt { a^2 \;+\; b^2 } } { 2 } }$$

Diagonal of a Rectangle formula

$$\large{ D' = \sqrt { a^2 \;+\; b^2 } }$$

Perimeter of a Rectangle formula

$$\large{ P= 2a \;+\; 2b }$$

$$\large{ P= 2 \left( a \;+\; b \right) }$$

Side of a Rectangle formula

$$\large{ a = \frac {P} {2} \;-\; b }$$

$$\large{ b = \frac {P} {2} \;-\; a }$$

Distance from Centroid of a Rectangle formula

$$\large{ C_x = \frac { b } { 2 } }$$

$$\large{ C_y = \frac { a } { 2} }$$

Elastic Section Modulus of a Rectangle formula

$$\large{ S_x = \frac { a^2b } { 6 } }$$

$$\large{ S_y = \frac { ab^2 } { 6 } }$$

Plastic Section Modulus of a Rectangle formula

$$\large{ Z_x = \frac { a^2b } { 4 } }$$

$$\large{ Z_y = \frac { ab^2 } { 4 } }$$

Polar Moment of Inertia of a Rectangle formula

$$\large{ J_{z} = \frac {ab}{12} \left( a^2 \;+\; b^2 \right) }$$

$$\large{ J_{z1} = \frac {ab}{3} \left( a^2 \;+\; b^2 \right) }$$

Radius of Gyration of a Rectangle formula

$$\large{ k_{x} = \frac { a } { 2 \sqrt 3 } }$$

$$\large{ k_{y} = \frac { b } { 2 \sqrt 3 } }$$

$$\large{ k_{z} = \sqrt \frac { a^2 \;+\; b^2 } { 2 \sqrt 3 } }$$

$$\large{ k_{x1} = \frac { a } { \sqrt 3 } }$$

$$\large{ k_{y1} = \frac { b } { \sqrt 3 } }$$

$$\large{ k_{z1} = \sqrt \frac { a^2 \;+\; b^2 } { \sqrt 3 } }$$

Second Moment of Area of a Rectangle formula

$$\large{ I_{x} = \frac {a^3b}{12} }$$

$$\large{ I_{y} = \frac {ab^3}{12} }$$

$$\large{ I_{x1} = \frac {a^3b}{3} }$$

$$\large{ I_{y1} = \frac {ab^3}{3} }$$

Torsional Constant of a Rectangle formula

$$\large{ J = a^3 b \left[ \frac {16}{3} \;-\; \frac {3.36a}{b} \left( 1 \;-\; \frac { a^4 } { 12b^4 } \right) \right] }$$

Where:

$$\large{ A_{area} }$$ = area

$$\large{ a, b }$$ = side

$$\large{ A, B, C, D }$$ = vertex

$$\large{ C }$$ = distance from centroid

$$\large{ D' }$$ = diagonal

$$\large{ I }$$ = moment of inertia

$$\large{ J }$$ = torsional constant

$$\large{ k }$$ = radius of gyration

$$\large{ P }$$ = perimeter

$$\large{ r }$$ = incircle

$$\large{ R }$$ = outcircle

$$\large{ S }$$ = elastic section modulus

$$\large{ Z }$$ = plastic section modulus