Line ab and cd are tangent to the circle and abcd is a rectangle with the side lengths 2x and 5x. What is the area of the shaded region

Question

Line ab and cd are tangent to the circle and abcd is a rectangle with the side lengths 2x and 5x. What is the area of the shaded region

Answer 1

To find the area of the shaded region, you must subtract the area of the circle from the area of the rectangle. Since the sides of the rectangle are 2x and 5x, it has an area of 2x * 5x=10x². The circle has a diameter of 2x, so the radius of the circle is x. The area of the circle is ∏x². So the shaded area has a region of 10x² -∏x² .