Rectangle Area Calculator: Find the Area of a Rectangle

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Rectangle — is a quadrangle in which all angles are straight (equal to 90 degrees). In Euclidean geometry, for a quadrilateral to be a rectangle, it is enough that at least three of its angles are straight, then the fourth angle, by the theorem on the sum of the angles of a polygon, will also be 90 °.

A rectangle is a four-sided polygon with opposite sides that are parallel and equal in length. The area of a rectangle is the product of its length and width. The formula for finding the area of a rectangle is:

A = l x w

where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle. This formula works for any rectangle, whether it's a perfect square or a more general rectangle with unequal sides.

How to Use the Rectangle Area Calculator

Our calculator makes it easy to find the area of your rectangle. You can use the calculator to find the area of a rectangle by entering its side lengths or its diagonals and the angle between them. Here's how to use the calculator:

Using our rectangle area calculator is simple. Follow these steps:

1. Choose the type of calculation you want to perform (by sides or by diagonals and angle).
2. Enter the required measurements for your calculation.
3. That's it, our calculator will automaticaly give you the area of your rectangle with formula.

Rectangle Area Formulas

The formula for finding the area of a rectangle through its sides is:

S = a*b

1. S - rectangle area
2. a - width of the rectangle
3. b - length of the rectangle

So, if you know the length and width of your rectangle, you can easily find its area using this formula.

The formula for finding the area of a rectangle through its diagonals and the angle between them:

S = \dfrac{d^2}{2}sin(\alpha)

Where:

1. S - rectangle area
2. d - diagonal of the rectangle
3. α - angle between diagonals

This formula comes from using the fact that a rectangle can be split into two congruent right triangles. So, if you know the diagonals and angle between them, you can easily find its area using this formula.

Rectangle Area Examples

Here are some examples of finding the area of a rectangle using our calculator:

Example 1: Find the area of a rectangle by its sides

Suppose we have a rectangle with a length of 12 units and a width of 6 units. To find its area using our calculator:

1. Choose the `By the sides` calculation type.
2. Enter 12 for the length and 6 for the width.

The calculator will display the area of the rectangle, which in this case is 72 square units.

Example 2: Find the area of a rectangle by its diagonals and angle

Suppose we have a rectangle with diagonals of length 10 units, and an angle of 60ᵒ degrees between them. To find its area using our calculator:

1. Choose the `By diagonals and angle` calculation type.
2. Enter 10 for the diagonal.
3. Enter 60ᵒ for the angle between the diagonals.

The calculator will display the area of the rectangle, which in this case is 43.3 square units.

Conclusion

Calculating the area of a rectangle is an important skill in geometry. Our rectangle area calculator and formula make it easy to find the area of your rectangle. Try it out for yourself and see how easy it can be!