The area of the smallest (shaded) square measures 1 square unit. What is the area of the largest square? (there are 7 squares)
Please, please, please help me!!!
uh... 7...
More information needed. We have no access to your diagram.
To find the area of the largest square, we need to understand the relationship between the sizes of the squares. Since the area of the smallest (shaded) square is given as 1 square unit, we can use this information to determine the pattern and calculate the area of the largest square.
Let's assign a variable to represent the length of the sides of each square. Suppose we use "x" as the variable to represent the side length of the smallest square. Then, we can determine the side length of each subsequent square based on this pattern:
1. The side length of the second square will be x + x/2, or 1.5x. (x + x/2 can be simplified to (3/2)x)
2. The side length of the third square will be (3/2)x + x/2, or 2x.
3. The side length of the fourth square will be 2x + x/2, or (5/2)x.
4. The side length of the fifth square will be (5/2)x + x/2, or 3x.
5. The side length of the sixth square will be 3x + x/2, or (7/2)x.
6. The side length of the seventh (largest) square will be (7/2)x + x/2, or 4x.
Now that we know the side length of the largest square is 4x, we can calculate its area:
Area of the largest square = (side length)^2
= (4x)^2
= 16x^2
Therefore, the area of the largest square is 16 square units.