# Area

Written by Jerry Ratzlaff on . Posted in Geometry

Area, 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 $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

Tags: Equations for Area