Examples with solutions for Powers: Using area

Exercise #1

A square has a side length of 8.

Calculate its area.

Video Solution

Step-by-Step Solution

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

  • Area=side length2 \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:
Area=82 \text{Area} = 8^2

Calculating 82 8^2 , we find:
8×8=64 8 \times 8 = 64

Thus, the area of the square is 64 64 .

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

Answer

64

Exercise #2

Given that the length of the sides of square 1 is 6

and the length of the side of square 2 is 7.

Which square has the larger area, 1 or 2?

Video Solution

Step-by-Step Solution

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:

Area=side length2 \text{Area} = \text{side length}^2

For square 1, the side length is 6:

Area1=62=36 \text{Area}_1 = 6^2 = 36

Step 2:

For square 2, the side length is 7:

Area2=72=49 \text{Area}_2 = 7^2 = 49

Step 3:

Now, compare the two areas:

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

Answer

2

Exercise #3

Given a square whose sides are 5. We draw another square whose sides are longer by 5 than the length of the sides of the previous square. Find the area of the new square.

Video Solution

Step-by-Step Solution

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:

New Side Length=5+5=10 units \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:

Area of the New Square=(Side Length)2=102=100 square units \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.

Answer

100

Exercise #4

A square has sides measuring 6 cm long. Another square has sides measuring 3 cm less than those of the previous square. Calculate the area of the new square.

Video Solution

Step-by-Step Solution

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 63=3 6 - 3 = 3 cm.
Step 3: The area of the new square is calculated using the formula Area=side2 \text{Area} = \text{side}^2 .
Thus, the new area is 32=9 cm2 3^2 = 9 \ \text{cm}^2 .

Therefore, the solution to the problem is 9 cm2 9 \ \text{cm}^2 .

Answer

9

Exercise #5

Given a square whose side length is 4. We draw a new square so that its side is 2 times bigger than the sides of the given square. Find the area of the new square.

Video Solution

Answer

64

Exercise #6

Given a square whose side length is 9.
A new square is formed with a side length that is three times smaller than the original.
Find the area of the new square.

Video Solution

Answer

9