Area Formulas

The standard notation for area is A.

Square

square

The area of a square of side a is:

A = a ⋅ a = a2

Rectangle

rectangle

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

A = a ⋅ b

Parallelogram

palallelogram

Let a pair of adjacent sides of the palellogram be a and b and altitudes ha and hb.
The parallelogram area is given by the formula:

A = a ⋅ ha = b ⋅ hb

Trapezoid

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:

$A = \frac{1}{2}(a + b)h$

Area of a circle

circle

$A = \pi\cdot r^2$

Area of a right triangle

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

triangle

with sides of length a, b, c and
altitudes ha, hb and hc.

A = ½(a ⋅ ha) = ½(b ⋅ hb) = ½(c ⋅ hc)
A = ½(ab ⋅ sin(∠C) = ½(ac ⋅ sin(∠B)) = ½(bc.sin(∠A))
p = ½(a + b + c)
A = √p(p - a)(p - b)(p - c) - Heron's formula
$A = R^2\sin(\angle A) \cdot \sin(\angle B) \cdot \sin(\angle C) = \frac{abc}{4R}$
where R is the radius of the prescribed circle.

Area of parallelogram, rhombus

Parallelogram

$A = AB\cdot DE = BC \cdot DF$
$A = AB \cdot AD \sin \alpha$
$A = \frac12 AC \cdot BD \sin \gamma$

Area of a quadrilateral

Parallelogram

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

Area of a regular polygon

Regular polygon

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

n is the number of edges(vertices).
$\pi=3.14159265359$


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