Calculating the Side and Diagonal Length of a Square Given its Area

In this article, we will explore how to determine the side length and the diagonal length of a square when given its area. We'll use a specific example to illustrate the process.

Understanding the Problem

Given the area of a square as 80 cm2, the goal is to find both the side length and the diagonal length of the square. This problem can be solved using basic algebra and the geometric properties of a square.

Step 1: Finding the Side Length

The formula for the area of a square is given by:

Area s2

Where s is the length of one side of the square. Given that the area is 80 cm2, we can set up the equation:

80 s2

To find s, we take the square root of both sides:

s √(80) √(16 * 5) 4√5 ≈ 8.94 cm

Step 2: Finding the Diagonal Length

The length of the diagonal d of a square can be found using the Pythagorean theorem or the formula:

d s√2

Substituting the value of s we found:

d 4√5 √2 4√10 ≈ 12.65 cm

Summary

The length of the side of the square is approximately 8.94 cm, and the length of the diagonal is approximately 12.65 cm.

Additional Examples

Example 1

Given the area of another square is 80 cm2, we can use the same process:

s √80 √(16 * 5) 4√5 ≈ 8.94 cm

The length of the diagonal is:

d 4√5 √2 4√10 ≈ 12.65 cm

Example 2

If the area of the square is 100 cm2, then:

s2 100 implies s 10 cm

The length of the diagonal is:

d s√2 10√2 ≈ 14.14 cm

Example 3

For yet another square with an area of 100 cm2, the side is:

Side √100 10 cm

The length of the diagonal is:

Diagonal 1.414 * 10 ≈ 14.14 cm

Conclusion

By understanding and applying the formulas for the area and diagonal of a square, you can easily solve for these measurements when given the area. This knowledge is useful in various real-world applications, such as construction, design, and geometry problems.