Plane Geometry The mathematical study of geometric figures whose parts lie in the same plane, such as lines, square, circle, triangle, rectangle, pentagon, polygon.


    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°.square
A square is a rectangle with equal sides
  Quadrilaterals include:

fig. 1  Square Area and Perimeter
A= S²
P= 4*S
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 = l*w.rectangle
It has perimeter P = 2*(l + w) = 2*l + 2*w
Each diagonal has length √( l ² + w ² )
In the diagram, p is a diagonal

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

  Speed Crunch  does not use implied multiplication. For multiplication you need to include the multiplication operator.
  example: [a * b]
  area = (base * height) or (b*h)
  perimeter = 2*(side a + side b) or 2*(a+b)

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


 Rhombus Information and Reference
    A rhombus is a four-sided shape where all sides have equal length. rhombusOpposite 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 = a*h
perimeter = 4*a
fig. 8  Rhombus Online Calculator
Reference: rhombus calculator
Reference: rhombus calculator


 Trapezoid Information and Reference

trapezoid    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.


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).
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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.
circle   In Speed Crunch Beside standard algebraic operator like + (addition), - (subtraction), * (multiplication), / (division), ^ or ** (exponentiation), there is support for some functions, for example sin, log, abs, and many more.
  You do not need to memorize function names, use Ctrl+F to pop up a dialog where you can choose the function that you need (more than 50 built-in math functions).   

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= (S ² * N)/(4 * tan (π/N))
        S= side length
        N= number of sides

In Speed Crunch If you want to recall again the expression which you typed before, then press up and down arrow to access the expression history. Moreover, your expression history (maximum last 100 expressions) is saved between sessions. This means you can still invoke those calculations you have done yesterday or last week.

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

   √ = sqrt(
   x² (or exponent 2) = X^2
   π = pi
Mathematical References and Formulas:
Kirt Blattenberger,Erie, PA, (814) 833-1967,
Dr. math forum
Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, 215-895-2000
Handbook of Mathematics
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an introduction to algebraic concepts for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.
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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 ...
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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.
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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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