Calculate Square Perimeter: Given Area = 3²√16 Square Units

To find the perimeter of the square ABCD, we first need to determine the side length of the square using the given area. The area of a square is calculated using the formula: $\text{Area} = s^2$, where $s$ is the side length of the square.

According to the problem, the area of the square is given by the expression $3^2\sqrt{16}$.

Let's simplify this expression:

• First, calculate $3^2$, which is $9$.

• Next, calculate $\sqrt{16}$, which is $4$.

Now, multiply these results: $9 \times 4 = 36$.

Thus, the area of the square is $36$.

Since the area is $s^2 = 36$, we can solve for $s$:

• Find the square root of both sides: $s = \sqrt{36}$.

• This gives $s = 6$.

Now that we have the side length $s = 6$, we can find the perimeter. The perimeter $P$ of a square is given by:

$P = 4s$.

Substituting the side length, we get:

• $P = 4 \times 6 = 24$.

The solution to the question is: $24$