Calculating Area and Perimeter of Rectangle

A rectangle is a plane, a quadrilateral that has 4 right angles. The sides that are parallel to each other are identical in length. If the rectangle has four equal sides, it is called a square. All squares are rectangles, but not all rectangles are squares. The perimeter of an object is the sum of all the lengths of the sides of that object. The area is the product of the length and the width of the object.

To find the area of a rectangle, calculate A = b h , where is the base (width) and is the height (length). The perimeter of a rectangle will always be P = 2 b + 2 h . If a rectangle is a square, with sides of length , then perimeter is P s q u a r e = 2 s + 2 s = 4 s and area is A s q a u r e = s ⋅ s = s 2 .

1 Ensure you are working with a true rectangle

Where the top and bottom lines are equal in length and the sides are equal in length. The top and bottom are parallel to each other, while the sides are also parallel to each other. In addition, the sides are perpendicular (exactly 90°) to the top and bottom lengths.

If all four sides of the object are identical, then you have a square. Squares are a type of rectangle.
If the object you are looking at does not meet these conditions, then it is not a rectangle.

2 Write down the formula for the area of a rectangle, A = l x w

In the formula for area (A), l is the length and w is the width of the rectangle. The units for area can be any unit for the measure of length squared: feet squared, meters squared, centimeters squared, etc.

You will see the units written as ft², m², cm², etc.

3 Identify the length and the width of the rectangle.

The length of the rectangle is equal to the top or bottom of the rectangle. The width is equal to the side of the rectangle. Using a ruler, measure each side of the rectangle to determine the length and the width.

In the above example, the length is 5 cm and the width is 2 cm.

4 Plug in the variables and solve the equation.

Using the length and width you just measured, plug them into the formula to solve for the area. Multiply the length times the width to calculate area.

For example, A = l x w = 5 x 2 = 10 cm².

Example

Basic Concepts of Area and Perimeter of a Rectangle

A rectangle is a quadrilateral with four right angles. The two sides of the rectangle are of equal length in pairs: the length and the width.

The general approach to calculating the area and perimeter of a rectangle includes:

Recognizing the standard form of the rectangle, with length (\( l \)) and width (\( w \)) as its sides.
Using formulas for calculating the area and perimeter based on the rectangle's dimensions.
Understanding how to apply these formulas to solve real-life problems involving rectangles.

Calculating the Area of a Rectangle

The area of a rectangle is the amount of space enclosed within its sides. The formula for the area is:

\[ \text{Area} = l \times w \]

Example:

If the length of a rectangle is \( 5 \) units and the width is \( 3 \) units, the area is:

Solution: \( \text{Area} = 5 \times 3 = 15 \) square units.

Calculating the Perimeter of a Rectangle

The perimeter of a rectangle is the total length of all its sides. The formula for the perimeter is:

\[ \text{Perimeter} = 2l + 2w \]

Example:

If the length of a rectangle is \( 5 \) units and the width is \( 3 \) units, the perimeter is:

Solution: \( \text{Perimeter} = 2(5) + 2(3) = 10 + 6 = 16 \) units.

Area and Perimeter Relationship

Both the area and perimeter are related to the dimensions of the rectangle. While the area represents the total space within the rectangle, the perimeter represents the distance around the rectangle.

Real-life Applications of Area and Perimeter of a Rectangle

Calculating the area and perimeter of a rectangle has many practical applications, such as:

Determining the amount of material needed to cover a rectangular surface (e.g., flooring, walls).
Finding the length of fencing required to enclose a rectangular garden.
Estimating the space available for storage in a rectangular room.

Common Operations with Rectangles

Area of a Rectangle: \( \text{Area} = l \times w \)

Perimeter of a Rectangle: \( \text{Perimeter} = 2l + 2w \)

Modifying Dimensions: If the length and width of a rectangle change, both the area and perimeter will be affected according to their respective formulas.

Area and Perimeter of Rectangle Examples Table
Problem Type	Description	Steps to Solve	Example
Calculating Area of a Rectangle	Finding the amount of space enclosed by a rectangle.	Use the formula: \( \text{Area} = l \times w \), where \( l \) is the length and \( w \) is the width. Multiply the length by the width to get the area.	For a rectangle with a length of 5 units and a width of 3 units, the area is \( 5 \times 3 = 15 \) square units.
Calculating Perimeter of a Rectangle	Finding the total length around the rectangle.	Use the formula: \( \text{Perimeter} = 2l + 2w \), where \( l \) is the length and \( w \) is the width. Add the lengths of all four sides to get the perimeter.	For a rectangle with a length of 5 units and a width of 3 units, the perimeter is \( 2(5) + 2(3) = 10 + 6 = 16 \) units.
Changing Dimensions	How changing the dimensions affects the area and perimeter of a rectangle.	If the length or width of the rectangle changes, both the area and perimeter will change accordingly. Recalculate the area and perimeter using the new dimensions.	For a rectangle with a new length of 7 units and a width of 4 units, the area becomes \( 7 \times 4 = 28 \) square units, and the perimeter becomes \( 2(7) + 2(4) = 14 + 8 = 22 \) units.
Real-life Applications	Using the area and perimeter of rectangles in practical scenarios.	To calculate how much material is needed to cover a rectangular surface (e.g., floor tiling, wallpapering). To determine the amount of fencing required to enclose a rectangular garden.	For a room with dimensions 10 units by 6 units, the area for flooring is \( 10 \times 6 = 60 \) square units, and the perimeter for fencing is \( 2(10) + 2(6) = 20 + 12 = 32 \) units.