Useful formulae

|+ Common equations for area:
! Shape
! Equation
! Variables
|-
|Square
|

s^2\,\!

s

is the length of the side of the square.
|-
|Regular hexagon
|

\frac{3 \sqrt{3}}{2}s^2\,\!

s

is the length of one side of the hexagon.
|-
|Regular octagon
|

2(1+\sqrt{2})s^2\,\!

s

is the length of one side of the octagon.
|-
|Perfect Pentagon
|

2.5w^2\,\!

w

is the width of one side when all sides are equal.
|-
|Perfect Hexagon
|

4w^2\,\!

w

is the width of one side when all sides are equal.
|-
|Perfect Octagon
|

7w^2\,\!

w

is the width of one side when all sides are equal.
|-
|Perfect Nonagon
|

4.5w^2\,\!

w

is the width of one side when all sides are equal.
|-
|Any regular polygon
|

\frac{1}{2}a p \,\!

a

is the apothem, or the radius of an inscribed circle in the polygon, and

p

is the perimeter of the polygon.
|-
|Any regular polygon
|

\frac{P^2/n} {4 \cdot tan(\pi/n)}\,\!

P

is the Perimeter and

n

is the number of sides.
|-
|Any regular polygon
|

\frac{P^2/n} {4 \cdot tan(180^\circ/n)}\,\!

P

is the Perimeter and

n

is the number of sides.
|-
|Rectangle
|

l \cdot w \,\!

l

and

w

are the lengths of the rectangle's sides (length and width).
|-
|Parallelogram (in general)
|

b \cdot h\,\!

b

and

h

are the length of the base and the length of the perpendicular height, respectively.
|-
|Rhombus
|

\frac{1}{2}ab

a

and

b

are the lengths of the two diagonals of the rhombus.
|-
|Triangle
|

\frac{1}{2}b \cdot h \,\!

b

and

h

are the base and altitude (height), respectively.
|-
|Disk

\pi r^2 \,\!

r

is the radius.
|-
|Circle, Circular area
|

\pi r^2 \,\!

, or

\pi d^2/4 \,\!

r

is the radius and

d

the diameter.
|-
|Ellipse
|

\pi ab \,\!

a

and

b

are the semi-major and semi-minor axes, respectively.
|-
|Trapezoid
|

\frac{1}{2}(a+b)h \,\!

a

and

b

are the parallel sides and

h

the distance (height) between the parallels.
|-
|Total surface area of a Cylinder
|

2\pi r^2+2\pi r h \,\!

r

and

h

are the radius and height, respectively.
|-
|Lateral surface area of a cylinder
|

2 \pi r h \,\!

r

and

h

are the radius and height, respectively.
|-
|Total surface area of a Cone
|

\pi r (l + r) \,\!

r

and

l

are the radius and slant height, respectively.
|-
|Lateral surface area of a cone
|

\pi r l \,\!

r

and

l

are the radius and slant height, respectively.
|-
|Total surface area of a Sphere
|

4\pi r^2\,\!

\pi d^2\,\!

r

and

d

\frac{1}{2} r^2 \theta \,\!

r

and

\theta

are the radius and angle (in radians), respectively.
|-
|Square to circular area conversion
|

\frac{4}{\pi} A\,\!

A

is the area of the square in square units.
|-
|Circular to square area conversion
|

\frac{1}{4} C\pi\,\!

C

is the area of the circle in circular units.

A disk is the area enclosed in a circle. Often such area is called ''cross-sectional or ''circular '' area'' like a round cable cut in half!