Rectangle Calculator

Lets first understand, what is a rectangle and how we can find different properties of a rectangle?

Rectangle

A rectangle is a quadrilateral with four right angles and with equal opposite sides.

Rectangle can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal or a parallelogram containing a right angle.

A rectangle with four sides of equal length is a square. The term 'oblong' is used to refer to a non-square rectangle.

Properties of a rectangle

1. A rectangle is cyclic, that means all corners lie on a single circle.

2. A rectangle is equiangular, that means all its corner angles are of 90°.

3. A rectangle has two lines of reflectional symmetry and rotational symmetry of order 2.

4. A rectangle is rectilinear, that means its sides meet at right angles.

Formulas

Let the Length of the Rectangle be \(L\) units,

and the Width of the Rectangle be \(W\) units.

Diagonal of the Rectangle will be \(\sqrt{L^2 + W^2}\) units.

Perimeter of the Rectangle will be \(2(L + B)\) units.

Area of the Rectangle will be \(LB\) square units.

When \(L=W\), the rectangle is a square.

Theorems

1. Among all rectangles of a given perimeter, the square has the largest area.

2. The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle.

3. A parallelogram with equal diagonals is a rectangle.

4. The incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a time form a rectangle.

For calculating different properties of the rectangle using above rectangle calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.