# Area Formulas

The standard notation for **area** is A.

#### Square

The area of a square of side a is:

^{2}

#### Rectangle

If a is the length and b is the width of a rectangle its area is:

#### Parallelogram

Let a pair of adjacent sides of the palellogram be a and b
and altitudes h_{a} and h_{b}.

The parallelogram area is given by the formula:

_{a}= b ⋅ h

_{b}

#### Trapezoid

Let the lengths of the both parallel sides of a trapezoid be a and b and the
distance between them is h(the trapezoid altitude).

The area is given by the formula:

#### Area of a circle

$A = \pi\cdot r^2$

#### Area of a right triangle

$A=\frac{a\cdot b}{2}$

$A=\frac{c\cdot h_c}{2}$

#### Area calculator

**Enter the triangle:**

#### Area of a triangle

Let ABC be a triangle

with sides of length a, b, c and

altitudes h_{a}, h_{b} and h_{c}.

_{a}) = ½(b ⋅ h

_{b}) = ½(c ⋅ h

_{c})

A = ½(ab ⋅ sin(∠C) = ½(ac ⋅ sin(∠B)) = ½(bc.sin(∠A))

#### Area of parallelogram, rhombus

$A = AB\cdot DE = BC \cdot DF$

$A = AB \cdot AD \sin \alpha$

$A = \frac12 AC \cdot BD \sin \gamma$

#### Area of a quadrilateral

$A = \frac12 AC \cdot BD \sin \varphi $

#### Area of a regular polygon

$A = \frac14 n\cdot a^2 cot(\frac{\pi}{n})$

n is the number of edges(vertices).

$\pi=3.14159265359$