Answer :
Sure! Let's find the area of a square when its perimeter is given as 20 inches. Here's the step-by-step solution:
1. Understanding the Perimeter:
- The perimeter of a square is the total length around all four sides.
- Since a square has four equal sides, let's denote the length of one side as \( s \).
2. Perimeter Calculation:
- The perimeter \( P \) of a square can be written as:
[tex]\[ P = 4 \times s \][/tex]
- Given the perimeter is 20 inches, we can set up the equation as:
[tex]\[ 4 \times s = 20 \][/tex]
3. Solving for Side Length:
- To find the side length \( s \), we divide the total perimeter by 4:
[tex]\[ s = \frac{20}{4} \][/tex]
- Therefore:
[tex]\[ s = 5 \text{ inches} \][/tex]
4. Calculating the Area:
- The area \( A \) of a square is found by squaring the length of one side:
[tex]\[ A = s^2 \][/tex]
- Substituting the side length we found:
[tex]\[ A = 5^2 \][/tex]
- Therefore:
[tex]\[ A = 25 \text{ square inches} \][/tex]
So, the area of the square with a perimeter of 20 inches is 25 square inches.
1. Understanding the Perimeter:
- The perimeter of a square is the total length around all four sides.
- Since a square has four equal sides, let's denote the length of one side as \( s \).
2. Perimeter Calculation:
- The perimeter \( P \) of a square can be written as:
[tex]\[ P = 4 \times s \][/tex]
- Given the perimeter is 20 inches, we can set up the equation as:
[tex]\[ 4 \times s = 20 \][/tex]
3. Solving for Side Length:
- To find the side length \( s \), we divide the total perimeter by 4:
[tex]\[ s = \frac{20}{4} \][/tex]
- Therefore:
[tex]\[ s = 5 \text{ inches} \][/tex]
4. Calculating the Area:
- The area \( A \) of a square is found by squaring the length of one side:
[tex]\[ A = s^2 \][/tex]
- Substituting the side length we found:
[tex]\[ A = 5^2 \][/tex]
- Therefore:
[tex]\[ A = 25 \text{ square inches} \][/tex]
So, the area of the square with a perimeter of 20 inches is 25 square inches.
