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A **square** is a rectangle in which the length and width are equal. If the side length is denoted by $$s$$, then the area of the square is:

$$A = s^2$$

When the area is known and the side length is needed, the formula is solved for $$s$$ by taking the square root of both sides:

$$A = s^2$$

$$\sqrt{A} = \sqrt{s^2}$$

$$\sqrt{A} = s$$

Thus the side length formula is:

$$s = \sqrt{A}$$

The first formula gives the area when the side length is known; the second gives the side length when the area is known. Because the area must be positive, the principal (positive) square root is used.

Area of a Square

A site manager is verifying the surface dimensions of a square concrete equipment pad. If the side length of the pad is represented by $s$, state the mathematical formula the manager should use to determine the total area ($A$) of the pad.

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Based on the scenario and the geometric properties of a square, state the formula used to calculate the area ($A$) from the side length ($s$), the formula used to find the side length ($s$) from the area ($A$), and the specific name of the square root used in these professional calculations.

Digital Asset Standardization for Corporate Branding

Order the steps to solve $$A=s^2$$ for $$s$$.

Match each square term or formula with its meaning.

If a square has area $$A$$, its side length is $$s=\sqrt{A}$$.

Which formula gives the side length of a square with area $$A$$?

A square has area $$A$$ and side length $$s$$. Which formula finds $$s$$?

If a square has side length $$s$$, its area is _____

What must be true for a rectangle to be a square?

Question:
For a square, write the formulas for area and side length. Which square root is used?

Sample answer:
The area formula is $$A=s^2$$. The side length formula is $$s=\sqrt{A}$$. Use the principal (positive) square root because side length is positive.

Key points:
- Area: $$A=s^2$$
- Side length: $$s=\sqrt{A}$$
- Use the principal (positive) square root.
- A side length is positive.

Rubric:
Full credit: Gives both correct formulas and identifies the principal (positive) square root with a correct reason.

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