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Geometric Shapes - Areas

Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..

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Square

 

Square - area, side, diagonal

The area of a square can be calculated as

A = a2                            (1a)

The side of a square can be calculated as

a = A1/2                            (1b)

The diagonal of a square can be calculated as

d = a 21/2                        (1c)

Rectangle

Rectangle - area, diagonal

The area of a rectangle can be calculated as

A = a b          (2a)

The diagonal of a rectangle can be calculated as

d = (a2 + b2)1/2     (2b)

Parallelogram

Parallelogram - area and diagonals

The area of a parallelogram can be calculated as

A = a h

  = a b sin α                        (3a)

The diameters of a parallelogram can be calculated as

d1 = ((a + h cot α)2 + h2)1/2                      (3b)

d2 = ((a - h cot α)2 + h2)1/2                     (3b)

Equilateral Triangle

An equilateral triangle is a triangle in which all three sides are equal.

Equilateral triangle - area and height

The area of an equilateral triangle can be calculated as

A = a2/3 31/2                                 (4a)

The area of an equilateral triangle can be calculated as

h = a/2 31/2                              (4b)

Triangle

Triangle - area, height, radius

The area of a triangle can be calculated as

A = a h / 2  

  = r s                                 (5a)

r = a h / 2s                          (5b)

R = b c / 2 h                        (5c)

s = (a + b + c) / 2                     (5d)

x = s - a                           (5e)

y = s - b                           (5f)

z = s - c                          (5g)

Trapezoid

Trapezium - trapezoid - area, height

The area of a trapezoid can be calculated as

A = 1/2 (a + b) h  

  = m h                           (6a)

m = (a + b) / 2                      (6b)

Hexagon

Hexagon - area, diameter

The area of a hexagon can be calculated as

A = 3/2 a2 31/2                             (7a)

d = 2 a 

  =  2 / 31/2

  = 1.1547005 s                              (7b)

s = 31/2 / 2 d  

   = 0.866025 d                              (7c)

Circle

Crcle - area

 

The area of a circle can be calculated as

A = π/4 d2

  = π r2 

  = 0.785.. d2                       (8a)

C = 2 π r 

  =  π d                           (8b)

where

C = circumference

Sector and Segment of a Circle

Sector of Circle

Area of a sector of circle can be expressed as

A = 1/2 θr r2                            (9)

= 1/360 θd π r2

where

θr = angle in radians

θd = angle in degrees

Segment of Circle

Area of a segment of circle can be expressed as

A = 1/2 (θr - sin θr) r2

= 1/2 (π θd/180 - sin θd) r2                             (10)

Right Circular Cylinder

Lateral surface area of a right circular circle can be expressed as

A = 2 π r h                                      (11)

where

h = height of cylinder (m, ft)

r = radius of base (m, ft)

Right Circular Cone

Lateral surface area of a right circular cone can be expressed as

A = π r l

= π r (r2 + h2)1/2                                   (12)

where

h = height of cone (m, ft)

r = radius of base (m, ft)

l = slant length (m, ft)

Sphere

Lateral surface area of a sphere can be expressed as

A = 4 π r2                                    (13)

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