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
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