Understanding Square Area and Side Length

The question asks us to consider the relationship between the area of a square and its side length under a specific condition: when the side is 1 unit.

First, let's recall the formula for the area of a square. The area of a square is calculated by multiplying the side length by itself.

Area of a square = side × side = \(\text{side}^2\)

The question asks if the statement "The area of a square is equal to its side" is true, specifically when the side is 1 unit. Let's test this condition using the formula.

Given that the side of the square is 1 unit:

• Side = 1 unit

Now, let's calculate the area of the square with a side of 1 unit:

Area = \(\text{side}^2\)

Area = \(1^2\)

Area = \(1 \times 1\)

Area = 1 square unit

So, when the side of the square is 1 unit, its area is 1 square unit. The question asks if the area is equal to its side in this case.

• Calculated Area = 1
• Given Side = 1

Comparing the area and the side, we see that 1 is indeed equal to 1.

Therefore, the statement "The area of a square is equal to its side" is true when the side is 1 unit.

Now we need to determine how often this is true given the condition. The condition is fixed: "if the side is 1 unit". Every single time the side of a square is 1 unit, its area will mathematically be 1 square unit, and thus equal to its side. There are no exceptions to this mathematical relationship when the side is exactly 1 unit.

So, the statement "The area of a square is equal to its side, if the side is 1 unit" is always true because whenever the side meets the condition (being 1 unit), the area will necessarily equal the side.

Examining the Options

Let's look at the provided options in the context of our finding:

• Always: This implies that whenever the side is 1 unit, the area is equal to the side without fail. Our calculation confirms this.
• Sometimes: This would mean that sometimes when the side is 1 unit, the area equals the side, and sometimes it doesn't. This contradicts the fixed mathematical outcome for a side of 1.
• Often: Similar to 'Sometimes', this suggests variability when the side is 1 unit, which isn't the case.
• Never: This would mean that the area is never equal to the side when the side is 1 unit. This is directly contradicted by our calculation showing Area = 1 and Side = 1.

Based on our analysis, the statement is true whenever the condition (side = 1 unit) is met. This makes the statement "Always" true under the specified condition.

Revision Table: Square Area and Side

Additional Information: When Area Equals Side

It's interesting to consider when the area of a square equals its side length in general, not just when the side is 1. We want to find the value(s) of the side, \(s\), for which \(A = s\).

Using the area formula \(A = s^2\), we set Area equal to side:

To solve for \(s\), we can rearrange the equation:

Factor out \(s\):

This equation holds true if either factor is zero:

• \(s = 0\)
• \(s - 1 = 0 \implies s = 1\)

So, the area of a square is equal to its side length when the side is 0 units or 1 unit. A square with side 0 has area 0, and 0 = 0. A square with side 1 has area 1, and 1 = 1.

The question specifically focused on the case where the side is 1 unit. In that specific scenario, the equality \(A=s\) is always true.