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Area of Plane Shapes

	Triangle Area = ½b × h b = base h = vertical height			Square Area = a² a = length of side
	Rectangle Area = w × h w = width h = height			Parallelogram Area = b × h b = base h = vertical height
	Trapezoid (US) Trapezium (UK) Area = ½(a+b) × h h = vertical height			Circle Area = πr² Circumference=2πr r = radius
	Ellipse Area = πab			Sector Area = ½r²θ r = radius θ = angle in radians

Here is an example:

Example: What is the area of this rectangle?

The formula is:

Area = w × h
w = width
h = height

We know w = 5 and h = 3, so:

Area = 5 × 3 = 15

parallelogram = bh

trapezoid = h/2 (b₁ + b₂)

triangle =

one half times the base length times the height of the triangle

equilateral triangle =

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triangle given SAS (two sides and the opposite angle)= (1/2) a b sin C
triangle given a,b,c = sqrt

[s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron's formula)
regular polygon = (1/2) n sin(360°/n) S²
when n = # of sides and S = length from center to a corner

Surface area.

A = 4 πr 2

(sphere).

List of formulae

Common formulae for area:
Shape	Formula	Variables
Regular triangle(equilateral triangle)	$\tfrac14\sqrt{3}s^2\,\!$	$s$ is the length of one side of the triangle.
Triangle	$\sqrt{s(s-a)(s-b)(s-c)}\,\!$	$s$ is half the perimeter, $a$ , $b$ and $c$ are the length of each side.
Triangle	$\tfrac12 a b \sin(C)\,\!$	$a$ and $b$ are any two sides, and $C$ is the angle between them.
Triangle	$\tfrac12bh \,\!$	$b$ and $h$ are the base and altitude(measured perpendicular to the base), respectively.
Square	$s^2\,\!$	$s$ is the length of one side of the square.
Rectangle	$lw \,\!$	$l$ and $w$ are the lengths of the rectangle's sides (length and width).
Rhombus	$\tfrac12ab$	$a$ and $b$ are the lengths of the twodiagonals of the rhombus.
Parallelogram	$bh\,\!$	$b$ is the length of the base and $h$ is the perpendicular height.
Trapezoid	$\tfrac12(a+b)h \,\!$	$a$ and $b$ are the parallel sides and $h$ the distance (height) between the parallels.
Regular hexagon	$\tfrac32\sqrt{3}s^2\,\!$	$s$ is the length of one side of the hexagon.
Regular octagon	$2\left(1+\sqrt{2}\right)s^2\,\!$	$s$ is the length of one side of the octagon.
Regular polygon	$\frac{1}{4}nl^2\cdot \cot(\pi/n)\,\!$	$l$ is the side length and $n$ is the number of sides.
Regular polygon	$\frac{1}{4n}p^2\cdot \cot(\pi/n)\,\!$	$p$ is the perimeter and $n$ is the number of sides.
Regular polygon	$\frac{1}{2}nR^2\cdot \sin(2\pi/n) = nr^2 \tan(\pi/n)\,\!$	$R$ is the radius of a circumscribed circle, $r$ is the radius of an inscribed circle, and $n$ is the number of sides.
Regular polygon	$\tfrac12a p \,\!$	$a$ is the apothem, or the radius of an inscribed circle in the polygon, and $p$ is the perimeter of the polygon.
Circle	$\pi r^2\ \text{or}\ \frac{\pi d^2}{4} \,\!$	$r$ is the radius and $d$ the diameter.
Circular sector	$\tfrac12 r^2 \theta \,\!$	$r$ and $θ$ are the radius and angle (inradians), respectively.
Ellipse	$\pi ab \,\!$	$a$ and $b$ are the semi-major andsemi-minor axes, respectively.
Total surface area of a Cylinder	$2\pi r (r + h)\,\!$	$r$ 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	$\pi r (r + l) \,\!$	$r$ 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	$4\pi r^2\ \text{or}\ \pi d^2\,\!$	$r$ and $d$ are the radius and diameter, respectively.
Total surface area of an ellipsoid		See the article.
Total surface area of a Pyramid	$B+\frac{P L}{2}\,\!$	$B$ is the base area, $P$ is the base perimeter and $L$ is the slant height.
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.