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It looks like you're working on problem 15, which involves finding the area of a square. The diagonal of the square is given as 8 feet. We can solve for the area of the square using the diagonal.

For a square, the relationship between the diagonal \( d \) and the side length \( s \) is given by the formula:

\[
d = s\sqrt{2}
\]

So, to find the side length \( s \), we rearrange the formula:

\[
s = \frac{d}{\sqrt{2}}
\]

Substituting \( d = 8 \) feet:

\[
s = \frac{8}{\sqrt{2}} = \frac{8}{1.414} \approx 5.66 \, \text{feet}
\]

Now, the area \( A \) of a square is given by:

\[
A = s^2
\]

Substituting \( s \approx 5.66 \) feet:

\[
A = (5.66)^2 \approx 32.0 \, \text{square feet}
\]

So, the area of the square is approximately **32.0 square feet**.

Would you like any additional details or clarifications?

Here are 5 related questions to expand your understanding:

1. How would the area change if the diagonal was doubled?
2. What is the formula for finding the perimeter of the square using the side length?
3. How can you calculate the length of the diagonal of a square if only the area is given?
4. What is the relationship between the side length and the diagonal in other shapes, like a rectangle?
5. How would the problem change if the shape was a rectangle instead of a square?

**Tip:** When solving geometric problems involving squares, remember that the diagonal divides the square into two right-angled triangles. This can help in understanding how the diagonal relates to the side lengths.

Find the area of a square with a diagonal of 8 feet.

Learn how to find the area of a square with a diagonal of 8 feet using the Pythagoras Theorem and geometric formulas. This step-by-step solution explains the relationship between the diagonal and side length, suitable for students in Grades 6-8.

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