A square is placed in a circle of area (49π)cm^2 such that all four vertices of the square lie on the circumference of the circle. What is the area of the square?

It's always helpful to draw a diagram beforehand.Since we know the area of the circle is (49π)cm², we can work out the radius using A=πr² . Rearranging, we get r = 7cm. Add this information to our diagram. We can see the diameter of the circle is a diagonal of the square.This means we can use the Pythagorean Theorem to find the side of the square. Let the side of the square = x cm Diameter= 2* radius = 14 cmFrom the Pythagorean Theorem: x² + x² = 14² 2x²=196 x²=98We are trying to find the area of the square, which is the (side length of the square)², which in this case is 98. Therefore, the answer is 98cm²