Area

Written by Jerry Ratzlaff on . Posted in Geometry

 circumference 2Area, abbreviated as A, is the square units of a given plane.

 

 

 

 

 

 

 

 

Area formulas

\(\large{ A =  \pi \; r^2  }\)  (circle)
\(\large{ A =  \frac{ \pi \; d^2 }{ 4 }  }\)  (circle
\(\large{ A =  \frac{ C \; r }{ 2 }  }\)  (circle
\(\large{ A =  \frac{ C^2 }{ 4 \; \pi }  }\) (circle)  
\(\large{ A = \frac{a\;b \;-\; r \; l_a \;+\; s \; \left(r \;-\; h_s \right)  }{2 }   }\) (circle corner)
\(\large{ A =  \theta \;r^2  }\) (circle sector)
\(\large{ A =   \frac {r^2 \; \left( \theta  \;-\;  sin \; \theta   \right) }{ 2 }       }\) (circle segment)
\(\large{  A =  h \; \left(  \frac{c \;+\; a}{2 }  \right)   }\) (acute trapezoid)
\(\large{ A = \frac {h\;b} {2} }\) (acute triangle)
\(\large{ A = a^2 }\)  (cube face area)
\(\large{ A = 6\;a^2 }\)  (cube surface face area)
\(\large{ A = \pi \;a_a\; b_a }\) (ellipse)
\(\large{ A = \frac{a\;b}{2} \; \left( {\theta - atan\;\left[  \frac{  a\;-\;b \;sin\;\left(2\;\theta_1\right)  }{  a\;+\;b\;+\;\left(a\;-\;b\right)\;cos\left(2\;\theta_2\right)  } \right]  +  atan\;\left[  \frac{  a\;-\;b \;sin\;\left(2\;\theta_1\right)  }{  a\;+\;b\;+\;\left(a\;-\;b\right)\;cos\;\left(2\;\theta_2\right)  } \right]   }       \right)  }\) (ellipse sector)
\(\large{ A = \frac{c\;d}{4} \;  \left[ arccos \left( 1-\frac{2\;h}{c} \right) - \left( 1-\frac{2\;h}{c} \right) \; \sqrt{ \frac{4\;h}{c} } - \frac{4\;h^2}{c^2}     \right]    }\) (ellipse segment)
\(\large{ A = \frac{ \sqrt{3} }{4}\; a^2 }\) (equilateral triangle)
\(\large{ A =  \frac{ Q }{ v }   }\) (flow rate)
\(\large{ A =  \frac{ \pi \; r^2 }{2}   }\) (half circle)
\(\large{ A =   \pi \; \left(  R_o^2  - r_i^2  \right)    }\) (hollow circle)
\(\large{ A = \pi \; \left( a \; b - e \; f \right)  }\) (hollow ellipse)
\(\large{  A =  h  \left(  \frac  {c \;+\; a}  {2 }  \right)  }\) (isosceles trapezoid)
\(\large{ A = \frac {h\;b} {2} }\) (isosceles triangle)
\(\large{ A = \frac{1}{2} \; n \; r  }\) (kite)
\(\large{ A = \frac{2 \; L}{ C_l \; \rho \; v^2}   }\) (lift force)
\(\large{ A = \frac {h\;b} {2} }\) (oblique triangle)
\(\large{ A = \frac {h\;b} {2} }\) (obtuse triangle)
\(\large{ A = a\;h_a  }\) (parallelogram)
\(\large{ A = \frac{F}{p} }\) (pressure)
\(\large{ A =  \frac{ \pi \; r^2 }{4}   }\) (quarter circle)
\( \large{ A = a\;b  }\) (rectangle)
\(\large{ A = \frac {7} {4} \;a^2 \; \cot \;\left( \frac {180°} {7} \right)   }\) (regular heptagon)
\(\large{ A =   \frac {3}{2} \; \sqrt{3} \; a^2 }\) (regular hexagon)
\(\large{ A = \frac {a\;r}{2} }\) (regular pentagon)
\(\large{ A =  r^2 \; n \; tan  \left( \frac{180}{n}  \right)  }\) (regular polygon)
\(\large{ A = h \;a }\) (rhombus)
\(\large{ A = \frac {1} {2}\; b\;h }\) (right isosceles triangle)
\(\large{ A = \frac{1}{2} \; d \; \left( a + c \right)   }\) (right trapezoid)
\(\large{ A = \frac {a\;b} {2} }\) (right triangle)
\( \large{ A = a \; b - r^2 \; \left( 4 - \pi \right)  }\) (rounded corner rectangle)
\(\large{ A = \frac {h\;b} {2} }\) (scalene triangle)
\(\large{ A = a^2 }\) (square)
\(\large{ A = \frac{F}{\sigma} }\) (stress)
\(\large{ A = 2\; \pi \;r_i\; t }\)  (thin walled circle)
\(\large{  A =  h \; \left(  \frac{c \;+\; a}{2 }  \right)   }\) (trapezoid)
\(\large{ A = \frac{c \;+\; b}{2} \; h   }\) (tri-equilateral trapezoid)

Where:

 Units English Metric
\(\large{ A }\) = area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ l_a }\) = arc length \(\large{ in }\) \(\large{ mm }\)
\(\large{ s }\) = chord length \(\large{ in }\) \(\large{ mm }\)
\(\large{ C }\) = circumference \(\large{ in }\) \(\large{ mm }\)
\(\large{ cot }\) = cotangent \(\large{ dimensionless }\)  
\(\large{ n }\) = diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge \(\large{ in }\) \(\large{ mm }\)
\(\large{ \rho }\)  (Greek symbol rho) = density  \(\large{\frac{lbm}{ft^3}}\)  \(\large{\frac{kg}{m^3}}\)  
\(\large{ Q }\) = flow rate  \(\large{\frac{ft^3}{sec}}\) \(\large{\frac{m^3}{s}}\) 
\(\large{ F }\) = force \(\large{ lbf }\)  \(\large{N}\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ h_a }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ h_s }\) = segment height \(\large{ in }\) \(\large{ mm }\)
\(\large{ a_a }\) = length semi-major axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ b_a }\) = length semi-minor axis \(\large{ in }\) \(\large{ mm }\)
\(\large{ C_l }\) = lift coefficient \(\large{ dimensionless }\)      
\(\large{ L }\) = lift force \(\large{ lbf }\)   \(\large{N}\) 
\(\large{ \pi }\) = Pi  \(\large{ dimensionless \; constant }\)   
\(\large{ p }\) = pressure \(\large{\frac{lbf}{in^2}}\)  \(\large{Pa}\) 
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_i }\) = inside radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ R_o }\) = outside radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ sin }\) = sine \(\large{ dimensionless }\)    
\(\large{ tan }\) = tangent \(\large{ dimensionless }\)    
\(\large{ t }\) = thickness \(\large{ in }\) \(\large{ mm }\)
\(\large{ \sigma }\)  (Greek symbol sigma) = stress \(\large{\frac{lbf}{in^2}}\)  \(\large{Pa}\) 
\(\large{ v }\) = velocity \(\large{\frac{ft}{sec}}\)  \(\large{\frac{m}{s}}\) 

 

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Tags: Area Equations