Note that the figure is symmetric above and below the x-axis, so we could maximize the area
above the x-axis and double the answer. The equation for a semi-circle of radius 10 is y = . The base of the rectangle has length 2x and a height of y, so the area of the
rectangle is A = 2xy. Now, because y = , we can substitute into the area equation toget: A = 2x . Let’s take the derivative and set it equal to zero. We get: A′ = = 0. Now we solve for x: