The perimeter of a shape is the sum of its side lengths.
The area of the square is: [tex]\mathbf{\frac{L^2}{16}}[/tex]
The given parameter is:
[tex]\mathbf{Perimeter = L}[/tex]
Let the side length of the square be x.
So, we have:
[tex]\mathbf{Perimeter = 4x}[/tex]
Substitute L for Perimeter
[tex]\mathbf{4x = L}[/tex]
Divide both sides by 4
[tex]\mathbf{x = \frac L4}[/tex]
The area of a square of side x is:
[tex]\mathbf{Area = x^2}[/tex]
Substitute L/4 for x
[tex]\mathbf{Area = (\frac L4)^2}[/tex]
Open bracket
[tex]\mathbf{Area = \frac{L^2}{16}}[/tex]
Hence, the area of the square is: [tex]\mathbf{\frac{L^2}{16}}[/tex]
Read more about areas and perimeters at:
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