Calculating the Area of a Rectangle with a Given Square Perimeter

This article delves into the process of determining the area of a rectangle, given that it has the same perimeter as a square. Specifically, we explore a scenario where a square with a side length of 60 cm and a rectangle with a length of 80 cm share the same perimeter. We will walk through the necessary calculations step-by-step to arrive at the area of the rectangle.

Understanding the Given Information

Let's begin by summarizing the information provided:

The side length of the square is 60 cm. The length of the rectangle is 80 cm. The perimeter of the square and the rectangle are the same.

Calculating the Perimeter of the Square

First, we calculate the perimeter of the square:

Numerically, the perimeter of the square is given by:

Perimeter of the square 4 times; side length 4 times; 60 cm 240 cm

Using the Perimeter to Determine the Rectangle's Dimensions

Knowing that the perimeter of the rectangle is also 240 cm, we can use the perimeter formula for rectangles to determine the missing dimension, the width (b), of the rectangle:

Numerically, the perimeter of the rectangle is given by:

Perimeter of the rectangle 2 times; (length width)

Substituting the known perimeter and length:

240 2 times; (80 b)

240 160 2b

2b 240 - 160

2b 80

b 40 cm

Calculating the Area of the Rectangle

Now that we have the width of the rectangle, we can calculate its area:

Area of the rectangle length times; width 80 cm times; 40 cm 3200 cm2

Conclusion

In summary, by utilizing the given information and basic geometric principles, we determined that the area of the rectangle, with a length of 80 cm and a width of 40 cm, is 3200 cm2. This detailed process showcases the importance of understanding perimeter formulas and their applications in solving geometrical problems.

Key Takeaways:

The perimeter of a square is four times its side length. The perimeter of a rectangle is twice the sum of its length and width. Given the same perimeter, the dimensions of a rectangle can be determined by solving for its width.