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Properties of a Parallelogram
Properties of a Trapezoid
Properties of a Right-Triangle
Properties of a Rhombus
Properties of a Circular area
All Geometric Shapes tools

Properties of a Rectangle

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

This tool calculates the basic geometric properties of a rectangle. Enter below the shape dimensions. The calculated results will have the same units as your input. Please use consistent units for any input.

a =
b =
Geometric properties:
Area =
Perimeter =
Diagonal p =
Inradius Ri =
Circumradius Rc =
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Definitions

Geometry

Rectangle is a quadrilateral shape with two pairs of parallel sides, that meet each other at right angles. If all sides are equal the shape is a square. The area of a rectangle is given by the formula:

\[ A = a b \]

where a, b the lengths of the sides.

The perimeter of a rectangle is simply the sum of the lengths of all sides:

\[ P = 2\left(a+b\right) \]

The length of the diagonal, can be expressed in terms of the length of the sides, using the Pythagorean theorem on the right triangle with the diagonal as hypotenuse:

\[ p = \sqrt{a^2 + b^2} \]

shape geometry

It is not possible to inscribe a circle on a rectangle, that is tangent to all four sides, unless these are equals (shape is square). The largest circle, that can be enclosed to the shape, has a radius equal to:

\[ R_i = \frac{\min{\left(a;b\right)}}{2} \]

On the other hand, there is a circumscribed circle (a circle that passes through all vertices) for any rectangle. Its radius is equal to:

\[ R_c = \frac{p}{2} = \frac{\sqrt{a^2 + b^2}}{2} \]

where p the diagonal length.

See also
Properties of a Parallelogram
Properties of a Trapezoid
Properties of a Right-Triangle
Properties of a Rhombus
Properties of a Circular area
All Geometric Shapes tools