# Rectangle

on . Posted in Plane Geometry

• Rectangle (a two-dimensional figure) is a quadrilateral with two pair of parallel edges.
• 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.
• 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
• b = d
• ∠A = ∠B = ∠C = ∠D = 360°
• 4 interior angles are 90°
• 2 diagonals
• 4 edges
• 4 vertexs

### Area of a Rectangle formula

$$A_{area} \;=\; a\;b$$
Symbol English Metric
$$A_{area}$$ = area  $$in^2$$ $$mm^2$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Circumcircle Radius of a Rectangle formulas

$$R \;=\; D' \;/\;2$$

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

Symbol English Metric
$$R$$ = outside radius $$in$$ $$mm$$
$$D'$$ = diagonal $$in$$ $$mm$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Diagonal of a Rectangle formula

$$D' \;=\; \sqrt {a^2 + b^2 }$$
Symbol English Metric
$$D'$$ = diagonal $$in$$ $$mm$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Distance from Centroid of a Rectangle formulas

$$C_x \;=\; b \;/\; 2$$

$$C_y \;=\; a \;/\; 2$$

Symbol English Metric
$$C$$ = distance from centroid $$in$$ $$mm$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Elastic Section Modulus of a Rectangle formulas

$$S_x \;=\; a^2\; b \;/\; 6$$

$$S_y \;=\; a\;b^2 \;/\; 6$$

Symbol English Metric
$$S$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Perimeter of a Rectangle formulas

$$P \;=\; 2\;a + 2\;b$$

$$P \;=\; 2\; ( a + b)$$

Symbol English Metric
$$P$$ = perimeter $$in$$ $$mm$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Plastic Section Modulus of a Rectangle formulas

$$Z_x \;=\; a^2 \;b \;/\; 4$$

$$Z_y \;=\; a\;b^2 \;/\; 4$$

Symbol English Metric
$$Z$$ = plastic section modulus $$in^3$$ $$mm^3$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Polar Moment of Inertia of a Rectangle formulas

$$J_{z} \;=\; (a\;b\;/\;12) \; ( a^2 + b^2 )$$

$$J_{z1} \;=\; (a\;b\;/\;3) \; ( a^2 + b^2 )$$

Symbol English Metric
$$J$$ = torsional constant $$in^4$$ $$mm^4$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Radius of Gyration of a Rectangle formulas

$$k_{x} \;=\; a \;/\; 2 \; \sqrt{3}$$

$$k_{y} \;=\; b \;/\; 2 \; \sqrt{3}$$

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

$$k_{x1} \;=\; a \;/\; \sqrt{3}$$

$$k_{y1} \;=\; b \;/\; \sqrt{3}$$

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

Symbol English Metric
$$k$$ = radius of gyration $$in$$ $$mm$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Second Moment of Area of a Rectangle formulas

$$I_{x} \;=\; a^3\; b\;/\;12$$

$$I_{y} \;=\; a\;b^3\;/\;12$$

$$I_{x1} \;=\; a^3 \;b\;/\;3$$

$$I_{y1} \;=\; a\;b^3\;/\;3$$

Symbol English Metric
$$I$$ = moment of inertia $$in^4$$ $$mm^4$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$

### Side of a Rectangle formulas

$$a \;=\; (P\;/\;2) - b$$

$$b \;=\; (P\;/\;2) - a$$

Symbol English Metric
$$a, b, c, d$$ = edge $$in$$ $$mm$$
$$P$$ = perimeter $$in$$ $$mm$$

### Torsional Constant of a Rectangle formula

$$J \;=\; a^3\; b\; [\; \frac{1}{3} - (0.21\;a\;/\;b) \; ( 1 - [ a^4 \;/\; 12\;b^4] \; ) \;]$$
Symbol English Metric
$$J$$ = torsional constant $$in^4$$ $$mm^4$$
$$a, b, c, d$$ = edge $$in$$ $$mm$$