A square is shown with a dashed segment from a vertex to the center. The dashed segment is 12 centimeters. What is the area of the square?
Let's call the side length of the square "s".
We know that the dashed segment is a radius of the circle that circumscribes the square. Since the radius is 12 centimeters, the diameter (which is equal to the diagonal of the square) must be 24 centimeters.
Using the Pythagorean theorem, we can find the length of a side of the square:
s² + s² = 24²
2s² = 576
s² = 288
s ≈ 16.97
So the area of the square is:
A = s²
A ≈ 288.01
Rounded to the nearest hundredth, the area of the square is 288.01 square centimeters.