If the Sides of a Square are Increased by 20%, How Does Its Area Change?
Imagine you have a beautiful garden with a square-shaped flower bed. One day, you decide to make it more spacious and increase the length of each side of the square by 20%. You might wonder how this change affects the area of your beloved flower bed. Let’s dive into the mathematics behind this intriguing question!
To embark on this mathematical journey, we first need to lay the foundation by understanding the concept of area.
Area of a Square
The area of a square is the region enclosed within its four equal sides. It is calculated by multiplying the length of one side by itself, i.e., Area = side length × side length.
Let’s denote the original side length of the square as ‘s’ units. Therefore, the original area of the square would be Area = s × s square units.
Increasing Side Length by 20%
When you increase the side length by 20%, you are essentially adding 20% of the original side length to each side. Mathematically, the new side length becomes 1.2s units, where 1.2 represents the 120% of the original side length.
New Area of the Square
Using the same formula for the area of a square, we can calculate the new area after increasing the side length. The new area becomes Area = 1.2s × 1.2s = 1.44s² square units.
Comparing the new area (1.44s²) with the original area (s²), we can see that the area has increased by a factor of 1.44. This means that the new area is 144% of the original area.
Example
Let’s illustrate this concept with an example. Suppose your original square flower bed had sides of 5 meters. After increasing the side length by 20%, the new side length becomes 6 meters (1.2 × 5). The new area of the flower bed is 36 square meters (6 × 6), which is 144% of the original area of 25 square meters (5 × 5).
In Conclusion
Therefore, increasing the side length of a square by 20% results in an increase in its area by 144%. This mathematical principle can be applied in various real-world scenarios, from designing gardens to calculating construction materials.
We invite you to explore this topic further and delve into the fascinating world of geometry. If you have any questions or would like to share your insights, feel free to leave a comment below.
Frequently Asked Questions (FAQ)
- What is the formula for the area of a square?
Area = side length × side length - What is the percentage increase in area if each side of a square is increased by 20%?
144% - How do you calculate the new side length if the original side length is increased by 20%?
New side length = Original side length × 1.2
