Rectangle Area

What is a Rectangle?

A rectangle is a closed polygon with four sides and four vertices, whose interior angles are right angles (90°). Opposite sides are parallel and equal in length. A rectangle is similar to a square, except that its two pairs of parallel sides may have different lengths.

How to Calculate the Area of a Rectangle

The area of a rectangle represents the number of square units inside a rectangle. To calculate this area, you need to know the length of its sides, i.e., the length of each line connecting two vertices of the rectangle.

Formula to Calculate the Area of a Rectangle

Practical Example

Let's say we need to calculate the area of a rectangle, and we are given the values of its sides, with a = 4 cm and b = 3 cm.

Replacing the values of its sides in the area formula

If we already have the lengths of the sides that make up the rectangle, calculating the area is as simple as replacing these values in the rectangle area formula. Thus, we have:

Calculating the area of a rectangle based on its diagonal and the length of one of its sides

In some problems, we are given only the length of the diagonal and one side of the rectangle. In these cases, we can use the Pythagorean theorem to determine the missing side and then apply the rectangle area formula above.

Pythagorean Theorem formula applied to a rectangle

Since the exercise statement gives us the length of the diagonal and the length of one of its sides, we can obtain the following equation:

By rearranging the "missing side" in the equation, we have the following relationship:

This relationship applies to all rectangles and will allow you to obtain the length of the side that you need to know. Once you find this value, you can apply the rectangle area formula without any problems as mentioned in the yellow box at the beginning of this article.