The area of the smallest (shaded) square measures 1 square unit. What is the area of the largest square? (there are 7 squares)

Please help me!!!

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To find the area of the largest square, we first need to understand the relationship between the squares and their areas.

Since the area of the smallest square is 1 square unit, we can assume that its side length is also 1 unit, as the area of a square is calculated by multiplying its side length by itself.

Now, let's examine the relationship between the side lengths of the squares. The side length of the next square is double that of the previous square. In other words, if the side length of the smallest square is 1 unit, then the side length of the next square will be 2 units, the next square will be 4 units, and so on.

This means that the side length of each square is essentially the base length of the square immediately before it, multiplied by 2.

To find the area of each square, we square the side length.
Therefore, the areas of the squares will increase exponentially, following a pattern of 1^2, 2^2, 4^2, 8^2, 16^2, 32^2, and 64^2.

Now, let's calculate the area of the largest square by squaring its side length.

The side length of the largest square is obtained by multiplying the previous side length (32) by 2.
So, the side length of the largest square is 32 * 2 = 64 units.

To find the area, we square the side length:
Area of the largest square = 64^2 = 4,096 square units.

So, the area of the largest square is 4,096 square units.