Area of the Square: Identify the greater value

To solve this problem, we will calculate the area of each square and compare them:

• Step 1: Calculate the area of square 1.
• Step 2: Calculate the area of square 2.
• Step 3: Compare the areas to find which square has a larger area.

Let's work through these steps:

Step 1:

The area of a square is calculated using the formula:

$\text{Area} = \text{side length}^2$

For square 1, the side length is 6:

$\text{Area}_1 = 6^2 = 36$

Step 2:

For square 2, the side length is 7:

$\text{Area}_2 = 7^2 = 49$

Step 3:

Now, compare the two areas:

$36$ (Area of square 1) is less than $49$ (Area of square 2).

Therefore, square 2 has a larger area.

Based on our calculations, the square with the larger area is square 2.

To determine which shape has a larger area, we need to compare the areas of the square and the rectangle:

• Step 1: Calculate the area of the original square:

The side length of the square is $X$, so its area is given by:

$\text{Area of square} = X^2$

• Step 2: Calculate the area of the rectangle:

The dimensions of the rectangle are $X + 3$ cm and $X - 3$ cm. Thus, its area is:

$\text{Area of rectangle} = (X + 3)(X - 3)$

Using the difference of squares formula, we find:

$(X + 3)(X - 3) = X^2 - 9$

• Step 3: Compare the areas:

We compute the difference between the square's area and the rectangle's area:

$X^2 - (X^2 - 9) = 9$

Since 9 is positive, the area of the square is larger than the area of the rectangle.

Therefore, the square has a larger area than the rectangle.