5 Ways to Find the Area of a Rectangle

Determining the area of a rectangle is a fundamental concept in geometry and is used in various real-world applications. The area of a rectangle can be found using different methods, and in this article, we will explore five ways to calculate it.

Method 1: Using the Formula A = lw

The most common method to find the area of a rectangle is by using the formula A = lw, where A is the area, l is the length, and w is the width. This formula is straightforward and easy to apply. Simply multiply the length and width of the rectangle to get the area.

For example, if the length of a rectangle is 6 cm and the width is 4 cm, the area can be calculated as follows:

A = lw = 6 cm x 4 cm = 24 cm²

Method 2: Using the Formula A = (l + w)(l + w) - lw

Another method to find the area of a rectangle is by using the formula A = (l + w)(l + w) - lw. This formula may seem complex, but it can be useful when you know the perimeter of the rectangle and want to find the area.

First, calculate the sum of the length and width (l + w). Then, square this sum and subtract the product of the length and width (lw).

Using the same example as above, where l = 6 cm and w = 4 cm, we can calculate the area as follows:

l + w = 6 cm + 4 cm = 10 cm (l + w)(l + w) = 10 cm x 10 cm = 100 cm² A = (l + w)(l + w) - lw = 100 cm² - 24 cm² = 76 cm²

However, this method is not recommended as it is more complicated than the first method and can lead to errors.

Method 3: Using the Perimeter and One Side

When you know the perimeter of a rectangle and one side, you can use the following formula to find the area:

A = (P - 2s)s

where A is the area, P is the perimeter, and s is the length of one side.

First, calculate the perimeter of the rectangle using the formula P = 2l + 2w. Then, substitute the values into the formula A = (P - 2s)s.

Using the same example as above, where l = 6 cm and w = 4 cm, we can calculate the perimeter and area as follows:

P = 2l + 2w = 2 x 6 cm + 2 x 4 cm = 12 cm + 8 cm = 20 cm

Now, substitute the values into the formula A = (P - 2s)s, where s = 6 cm:

A = (P - 2s)s = (20 cm - 2 x 6 cm) x 6 cm = (20 cm - 12 cm) x 6 cm = 8 cm x 6 cm = 48 cm²

This method is more complicated than the first method and should only be used when the perimeter and one side are known.

Method 4: Using the Diagonal and One Side

When you know the diagonal and one side of a rectangle, you can use the following formula to find the area:

A = (¹⁄₂)d s

where A is the area, d is the diagonal, and s is the length of one side.

First, calculate the diagonal of the rectangle using the Pythagorean theorem: d = √(l² + w²). Then, substitute the values into the formula A = (¹⁄₂)d s.

Using the same example as above, where l = 6 cm and w = 4 cm, we can calculate the diagonal and area as follows:

d = √(l² + w²) = √(6 cm² + 4 cm²) = √(36 cm² + 16 cm²) = √52 cm² ≈ 7.21 cm

Now, substitute the values into the formula A = (¹⁄₂)d s, where s = 6 cm:

A = (¹⁄₂)d s = (¹⁄₂) x 7.21 cm x 6 cm ≈ 21.63 cm²

This method is more complicated than the first method and should only be used when the diagonal and one side are known.

Method 5: Using a Grid

When you are working with a rectangle that has whole number dimensions, you can use a grid to find the area. This method is useful for visualizing the rectangle and can help you understand the concept of area.

For example, if you have a rectangle with a length of 6 cm and a width of 4 cm, you can create a grid with 6 rows and 4 columns. Then, count the number of squares in the grid to find the area.

Using the same example as above, we can create a grid with 6 rows and 4 columns:

Row 1: ■ ■ ■ ■ Row 2: ■ ■ ■ ■ Row 3: ■ ■ ■ ■ Row 4: ■ ■ ■ ■ Row 5: ■ ■ ■ ■ Row 6: ■ ■ ■ ■

The total number of squares in the grid is 24. Therefore, the area of the rectangle is 24 cm².

📝 Note: The grid method is only useful for visualizing the rectangle and should not be used for calculations.

In conclusion, there are several ways to find the area of a rectangle. The most common method is by using the formula A = lw. Other methods include using the perimeter and one side, the diagonal and one side, or a grid. It is essential to choose the most suitable method based on the information given and the desired level of complexity.