Areas of Geometric Shapes

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

Square

 

square

A = a2     (1a)

a = A1/2    (1b)

d = a 21/2    (1c)

Rectangle

rectangle

A = a b          (2a)

d = (a2 + b2)1/2     (2b)

Parallelogram

parallelogram

A = a h

  = a b sin α       (3a)

d1 = ((a + h cot α)2 + h2)1/2    (3b)

d2 = ((a - h cot α)2 + h2)1/2    (3b)

Equilateral Triangle

equilateral triangle

A = a2/3 31/2    (4a)

h = a/2 31/2     (4b)

Triangle

 triangle

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

A = 1/2 (a + b) h  

  = m h       (6a)

m = (a + b) / 2      (6b)

Hexagon

hexagon

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

circle

 

A = π/4 d2

  = π r2 

  = 0.785.. d2        (8a)

U = 2 π r 

  =  π d      (8b)

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)

Related Topics

  • Mathematics - Mathematical rules and laws - areas, volumes, exponents, trigonometric functions and more

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