# Area of a rectangle

The area of a rectangle is the space contained within its perimeter. The grey space is the area of the rectangle in the diagram below.

## Area formula of a rectangle

The area, A, of a rectangle is the product of its length, l, and width, w.

A = l×w

*Note: Sometimes, base and height are used instead of length and width.*

### Area formula using the diagonal

If the diagonal, d, and one side, s, of the rectangle are known, the following area formula can be used:

Example:

Find the area of the rectangle below that has a diagonal of 26 and length of 24.

Since the area of a rectangle is a product of its length and width, we need to find the width. The diagonal of a rectangle divides it into two congruent right triangles. Using the Pythagorean theorem:

w^{2} + 24^{2} = 26^{2}

w^{2} + 576 = 676

w^{2} = 100

w = 10

The area of the rectangle is:

A = l×w = 24×10 = 240

Using the diagonal and side length formula:

A = | |

= | |

= | 24 × 10 |

= | 240 |

## Finding area using a grid

Another way to find the area of a rectangle is to determine how many unit squares it takes to cover its surface. Below is a unit square with length 1 cm.

A grid of unit squares can be used when determining the area of a rectangle.

The grid above contains unit squares that have an area of 1 cm^{2} each. The rectangle on the left contains 8-unit squares, so it has an area of 8 cm^{2}. The rectangle to the right contains 20-unit squares, so it has an area of 20 cm^{2}.