The area of a square is determined by:

The area of a square is determined by:

• A. length + width
• B. the perimeter squared
• C. the length of one side squared
• D. the sum of all sides

Answer: (C)

To determine the area of a square, you need to consider the definition of area in relation to the properties of a square. A square is a geometric figure with four equal sides. The formula for calculating the area of a square is derived from multiplying the length of one side by itself. In mathematical terms, if the length of one side of the square is represented as \(s\), then the area \(A\) can be expressed as: \[ A = s \times s = s^2 \] This means that the area is found by squaring the length of one side. Therefore, recognizing that the measurement necessary to calculate the area is linked directly to the length of a single side squared is essential in understanding the properties of squares. The other options suggest different approaches that do not fit the mathematical definition of area. For example, adding lengths or summing all sides does not yield the area measurement, and the perimeter squared would not represent the space contained within the square. Thus, the correct option is based on the fundamental formula for finding the area of a square, which is indeed the length of one side squared.

To determine the area of a square, you need to consider the definition of area in relation to the properties of a square. A square is a geometric figure with four equal sides. The formula for calculating the area of a square is derived from multiplying the length of one side by itself.

In mathematical terms, if the length of one side of the square is represented as (s), then the area (A) can be expressed as:

[ A = s \times s = s^2 ]

This means that the area is found by squaring the length of one side. Therefore, recognizing that the measurement necessary to calculate the area is linked directly to the length of a single side squared is essential in understanding the properties of squares.

The other options suggest different approaches that do not fit the mathematical definition of area. For example, adding lengths or summing all sides does not yield the area measurement, and the perimeter squared would not represent the space contained within the square. Thus, the correct option is based on the fundamental formula for finding the area of a square, which is indeed the length of one side squared.