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

Related Documents

Tag Search

  • en: geometry figures area shapes

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

close