Square Information and Reference
  A quadrilateral is a 2-dimensional closed shape with four straight sides. A Square is a quadrilateral with opposite sides parallel and all sides are equal in length and all angles are equal to 90°.
A square is a rectangle with equal sides
  Quadrilaterals include:

fig. 1  Square Area and Perimeter
A= S²
P= 4S
fig. 2  Square Online Calculator
Reference: Square Calculator
Reference: Square Calculator

 Rectangle Information and Reference
  A rectangle is any quadrilateral with four right angles. The two diagonals are equal in length and bisect each other.
  l = length of rectangle    w = width of rectangle
It has area A = lw.
It has perimeter P = 2l + 2w = 2(l + w)
Each diagonal has length √( l² + w² )
In the diagram, p is a diagonal
  In RedCrab several math expressions can be written in a row. Between each math expression, there must be a colon.
        Note : l = 6: w = 5

fig. 3  Rectangle Area and Perimeter
Area = lw
Perimeter = 2l+2w
fig. 4  Rectangle Online Calculator
Reference: Rectange Calculator
Reference: Rectangle Calculator

 Parallelogram Information and Reference

   A parallelogram is a four-sided shape where opposite sides are parallel and equal in length, and opposite angles are equal

  RedCrab interprets a series of letters, for example, ab, as different variables (as a and b). It also features implied multiplication. Implied multiplication means you do not need to include the multiplication operator.
  example: [a * b = ab]
  area = (base * height) or (bh)
  perimeter = 2(side a + side b) or 2(a+b)

fig. 5  Parallelogram Area and Perimeter
Area = (bh)
Perimeter = 2(side a + side b)
fig. 6  Parallelogram Online Calculator
Reference: Parallelogram calculator
Reference: Parallelogram calculator

 Rhombus Information and Reference
  area = (side a * hei,ght) or (ah)
  perimeter = 4(side a) or 4a

    A rhombus is a four-sided shape where all sides have equal length. Opposite sides are parallel and opposite angles are equal. Also the diagonals (dashed lines in the figure) of a rhombus bisect each other at right angles.

Reference: rhombus area
Reference: rhombus perimeter

fig. 7  Rhombus Area and Perimeter
area = ah
perimeter = 4a
fig. 8  Rhombus Online Calculator
Reference: rhombus calculator
Reference: rhombus calculator

 Trapezoid Information and Reference

   a trapezoid is a quadrilateral with only one pair of opposite sides parallel and the parallel sides are called bases and the nonparallel sides are called legs.

In RedCrab, you can write several mathematical expressions on one work sheet. The expressions result displays only if terminated with equal sign.
   X = 17 + 4 = 21
   X = 17 + 4

fig. 9  Trapezoid Area and Perimeter
Area = (a + b)/2*h
Perimeter = a + b + c + d
fig. 10  Trapezoid Online Calculator
Reference: Trapezoid Area
Reference: Trapezoid Calculator

Triangle Information and Reference

    The right triangle has one 90 degree angle and two acute . . . (< 90 degree) angles. The sum of the angles of a triangle is always 180 degrees. The two sides of the triangle that are by the right angle are called the legs... and the side opposite of the right angle is called the hypotenuse.
   Side b = base;   Side a = height
  In the equilateral triangle, all the sides are the same length (congruent) and all the angles are the same size (congruent).
  The isosceles triangle has two sides that are the same length (congruent) and two angles that are the same size (congruent).

Reference: Triangle Calculator
Reference: Triangle Calculator

fig. 11  Triangle Area
   Area = (1/2)bh
   Perimeter = a+b+c
fig. 12  Triangle Online Calculator
   Reference: Triangle
   Reference: Triangle

 Kite Information and Reference

  In geometry (a quadrilateral is a polygon with four sides (or 'edges') and four vertices or corners). A kite is a quadrilateral with two pairs of adjacent, congruent sides.
  To find the area of a kite, multiply the lengths of the two diagonals and divide by 2. To find the perimeter of a kite, just add half the lengths of the sides and multiply by 2.

  f = short diagonal   g = long diagonal
  side ab = side dc
  angle B = angle D

fig. 13  Kite Area
   Area = (fg)/2
   Perimeter = 4πR²
fig. 14  Kite Online Calculator
   Reference: Kite Calculator
   Reference: Kite Calculator

 Circle Information and Reference
  A circle - A plane curve everywhere equidistant from a given fixed point, the center.

  In RedCrab, with Result boxes you can display formatted results of calculations on any work sheet position. Click Result box on the Insert menu to open a result box.
  A result box can be displayed on any position. So you can insert results directly on technical drawings. Result text can be displayed vertically, horizontally or inclined position. The size of the box is auto fitted to the size of the text.

fig. 15  Circle Area
   Area = πR²
   Circumference = 2πR
fig. 16  Circle Information and Reference
Reference: Circle Area
Reference: Circle Area

 Pentagon Information and Reference
   A Pentagon is a five-sided polygon. The sum of the angles of a pentagon is 540 degrees. The angles in the center are 72 degrees (360/5) = 72

  N = number of sides
  S = side length
  Area aprox. = S² * 1.720477401
  or Area = S²N / (4tan(π/N))
   Reference: Pentagon formulas
   Reference: Pentagon formulas
   Reference: Pentagon Area and Perimeter

fig 17  Pentagon Area and Perimeter
   Area = S²N / (4tan(π/N))
   Perimeter = 5 S
fig 18  Pentagon Information and Reference
   Reference: Pentagon Area and Perimeter
   Reference: Pentagon Area and Perimeter

Hexagon Information and Reference

  Regular Hexagon - a hexagon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
  ∠ = angle    ∠ 30  read as: angle 30
     ∠ A = ∠ B = ∠ C = ∠ D = ∠ E = ∠ F

  AB = line segment AB
     AB = BC = CD = DE = EF = FA

   Reference: Hexagon Calculators
   Reference: Hexagon Calculators

fig. 19  Hexagon Area and Perimeter
   Area = (3√3)/2 S²
   Perimeter = 6 S
fig. 20  Hexagon Online Calculator
   Reference: Hexagon Calculator
   Reference: Hexagon Calculator

 Polygon Information and Reference
    Using an Octagon as example:

 Polygon area formula:
     A= S² N/4(tan(π/N))
        S= side length
        N= number of sides

   Reference: Polygon Calculator
   Reference: Polygon Calculator
   Reference: Octagon Calculator

fig. 21  Polygon Area and Perimeter
   Area = 2(1+√2)S²
   Perimeter = 8 S
fig. 22  Polygon Online Calculator
   Reference: Polygon Calculator
   Reference: Polygon Calculator

   √ = Crtl + 1
   x² (or exponent 2) = F3 + 2
   π = Ctrl + P
Mathematical References and Formulas:
Kirt Blattenberger,Erie, PA, (814) 833-1967, rfcafe@earthlink.net
Dr. math forum
Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, 215-895-2000
Handbook of Mathematics
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Algebra I
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Plane Geometry
Plane Geometry Formulas. Rectangle: Square: Perimeter: P = 2L + 2W ... Perimeter: add the lengths of all sides. Circumference: C = 2. ? r. Area: A = 2H. B. Area: A ...
Foundations of geometry for university students and high-school students
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry.
Plane Geometry
For a generation this was the leading textbook on the subject of plane geometry in America. Topics covered: rectilinear figures, the circle, proportion, similar polygons, areas of polygons, regular polygons and circles, etc.
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Areas of Plane Figures.
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CRC Standard Mathematical Tables and Formulas
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Wire Resistance and Voltage Drop Calculator
The National Electric Code (NEC) specifies the following formula to determine acceptable wire size in circular mils (CM) for a constant load of I amps, wire length L in feet, and voltage drop V.
      CM = (25 x I x L) / V
      V = (25 x I x L) / CM
  NEC has established that a 2% maximum voltage drop is acceptable.

The resistance, R, of a length of wire is described by the expression:
    R = pL/A
    p = resistivity of the material composing the wire,
    L = length of the wire, and
    A = area of the conducting cross section of the wire.

AWG (American Wire Gauge) Cable Description

Copper wire figures

Copper wire resistance table

AWG Feet/Ohm Ohms/100ft Ampacity* mm^2 Meters/Ohm Ohms/100M

    10      490.2         .204    30     2.588 149.5 .669
    12      308.7         .324    20     2.053 94.1 1.06
    14      193.8         .516    15     1.628 59.1 1.69
    16      122.3         .818    10     1.291 37.3 2.68

Specific resistance
Resistance and resistivity
Common Wire Gauges

p = 1.724 x 10-8 ohm m
Copper Wire Size and Characteristics @ 100 Degrees F
General Conductor Information dc Resistance
Voltage Drop Calculator
Voltage Drop Calculator
Voltage Drop Calculator
Voltage Drop Calculator
Voltage Drop Calculator
Minimum conductor size
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Copper Wire Resistance and Voltage Drop and Conductor Size Calculators