Powers: Using area

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 the area of a square with a side length of 8, we use the formula for the area of a square:

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

Let's perform the calculations step by step:
The side length given is 8. Substituting this value into the formula, we have:
$\text{Area} = 8^2$

Calculating $8^2$, we find:
$8 \times 8 = 64$

Thus, the area of the square is $64$.

Therefore, the solution to the problem is $64$. This result matches the correct choice provided, which is choice $64$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the original side length.
• Step 2: Determine the new side length by subtracting 3 cm from the original side length.
• Step 3: Apply the formula for the area of a square to find the area of the new square.

Now, let's work through each step:
Step 1: The original square has sides measuring 6 cm.
Step 2: The new square has sides measuring $6 - 3 = 3$ cm.
Step 3: The area of the new square is calculated using the formula $\text{Area} = \text{side}^2$.
Thus, the new area is $3^2 = 9 \ \text{cm}^2$.

Therefore, the solution to the problem is $9 \ \text{cm}^2$.

To solve this problem, let's follow these steps:

• Step 1: Determine the side length of the new square.
• Step 2: Calculate the area of the new square using the area formula for a square.

Now, let's work through the solution:

Step 1: Calculate the side length of the new square.

The side length of the original square is 5 units. The problem states that the side of the new square is longer by 5 units than the original square. Therefore, the side length of the new square is:

$\text{New Side Length} = 5 + 5 = 10 \text{ units}$

Step 2: Calculate the area of the new square.

To find the area of the new square, we use the formula for the area of a square, which is the side length squared:

$\text{Area of the New Square} = (\text{Side Length})^2 = 10^2 = 100 \text{ square units}$

Therefore, the area of the new square is 100 square units.

Thus, the correct answer is option 3: 100.