Common equations for area:
| Shape |
Equation |
Variables |
| Square |
Failed to parse (Missing texvc executable; please see math/README to configure.): s^2\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): s
is the length of the side of the square.
|
| Regular triangle |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\sqrt{3}}{4}s^2\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): s
is the length of one side of the triangle.
|
| Regular hexagon |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{3\sqrt{3}}{2}s^2\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): s
is the length of one side of the hexagon.
|
| Regular octagon |
Failed to parse (Missing texvc executable; please see math/README to configure.): 2(1+\sqrt{2})s^2\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): s
is the length of one side of the octagon.
|
| Any regular polygon |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2}a p \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): a
is the apothem, or the radius of an inscribed circle in the polygon, and Failed to parse (Missing texvc executable; please see math/README to configure.): p
is the perimeter of the polygon.
|
| Any regular polygon |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{P^2/n} {4 \cdot tan(\pi/n)}\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): P
is the Perimeter and Failed to parse (Missing texvc executable; please see math/README to configure.): n
is the number of sides.
|
| Any regular polygon (using degree measure) |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{P^2/n} {4 \cdot tan(180^\circ/n)}\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): P
is the Perimeter and Failed to parse (Missing texvc executable; please see math/README to configure.): n
is the number of sides.
|
| Rectangle |
Failed to parse (Missing texvc executable; please see math/README to configure.): l \cdot w \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): l
and Failed to parse (Missing texvc executable; please see math/README to configure.): w
are the lengths of the rectangle's sides (length and width).
|
| Parallelogram (in general) |
Failed to parse (Missing texvc executable; please see math/README to configure.): b \cdot h\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): b
and Failed to parse (Missing texvc executable; please see math/README to configure.): h
are the length of the base and the length of the perpendicular height, respectively.
|
| Rhombus |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2}ab |
Failed to parse (Missing texvc executable; please see math/README to configure.): a
and Failed to parse (Missing texvc executable; please see math/README to configure.): b
are the lengths of the two diagonals of the rhombus.
|
| Triangle |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2}b \cdot h \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): b
and Failed to parse (Missing texvc executable; please see math/README to configure.): h
are the base and altitude (measured perpendicular to the base), respectively.
|
| Triangle |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2}\cdot a \cdot b \cdot sinC\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): a
and Failed to parse (Missing texvc executable; please see math/README to configure.): b
are any two sides, and Failed to parse (Missing texvc executable; please see math/README to configure.): C
is the angle between them.
|
| Circle |
Failed to parse (Missing texvc executable; please see math/README to configure.): \pi r^2 \,\!
, or Failed to parse (Missing texvc executable; please see math/README to configure.): \pi d^2/4 \,\!
|
Failed to parse (Missing texvc executable; please see math/README to configure.): r
is the radius and Failed to parse (Missing texvc executable; please see math/README to configure.): d
the diameter.
|
| Ellipse |
Failed to parse (Missing texvc executable; please see math/README to configure.): \pi ab \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): a
and Failed to parse (Missing texvc executable; please see math/README to configure.): b
are the semi-major and semi-minor axes, respectively.
|
| Trapezoid |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2}(a+b)h \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): a
and Failed to parse (Missing texvc executable; please see math/README to configure.): b
are the parallel sides and Failed to parse (Missing texvc executable; please see math/README to configure.): h
the distance (height) between the parallels.
|
| Total surface area of a Cylinder |
Failed to parse (Missing texvc executable; please see math/README to configure.): 2\pi r^2+2\pi r h \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): r
and Failed to parse (Missing texvc executable; please see math/README to configure.): h
are the radius and height, respectively.
|
| Lateral surface area of a cylinder |
Failed to parse (Missing texvc executable; please see math/README to configure.): 2 \pi r h \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): r
and Failed to parse (Missing texvc executable; please see math/README to configure.): h
are the radius and height, respectively.
|
| Total surface area of a Cone |
Failed to parse (Missing texvc executable; please see math/README to configure.): \pi r (l + r) \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): r
and Failed to parse (Missing texvc executable; please see math/README to configure.): l
are the radius and slant height, respectively.
|
| Lateral surface area of a cone |
Failed to parse (Missing texvc executable; please see math/README to configure.): \pi r l \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): r
and Failed to parse (Missing texvc executable; please see math/README to configure.): l
are the radius and slant height, respectively.
|
| Total surface area of a Sphere |
Failed to parse (Missing texvc executable; please see math/README to configure.): 4\pi r^2\,\!
or Failed to parse (Missing texvc executable; please see math/README to configure.): \pi d^2\,\!
|
Failed to parse (Missing texvc executable; please see math/README to configure.): r
and Failed to parse (Missing texvc executable; please see math/README to configure.): d
are the radius and diameter, respectively.
|
| Total surface area of an ellipsoid |
|
See the article. |
| Circular sector |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{2} r^2 \theta \,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): r
and Failed to parse (Missing texvc executable; please see math/README to configure.): \theta
are the radius and angle (in radians), respectively.
|
| Square to circular area conversion |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{4}{\pi} A\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): A
is the area of the square in square units.
|
| Circular to square area conversion |
Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{4} C\pi\,\! |
Failed to parse (Missing texvc executable; please see math/README to configure.): C
is the area of the circle in circular units.
|
