Calculate Square Perimeter from Area Expression: (3²-1²)+2³

Given a square whose area is

$(3^2-1^2)+2^3$

What is the perimeter of this square?

To solve this problem, we need to find the perimeter of a square given its area. The area of the square is given by the expression $(3^2-1^2)+2^3$.

Let us evaluate the expression to find the area:

• Calculate $3^2$, which is $9$.
• Calculate $1^2$, which is $1$.
• Subtract to find $3^2 - 1^2 = 9 - 1 = 8$.
• Calculate $2^3$, which is $8$.
• Add the results: $8 + 8 = 16$.

Therefore, the area of the square is $16$.

In general, the area of a square is given by the formula $s^2$, where $s$ is the side length of the square. To find the side length, we solve the equation:

• $s^2 = 16$.
• Taking the square root of both sides, we find $s = \sqrt{16} = 4$.

The perimeter $P$ of a square with side length $s$ is given by the formula:

• $P = 4s$.

Thus, substituting the value of $s$:

• $P = 4 \times 4 = 16$.

Therefore, the perimeter of the square is $16$.