## Calculus 8th Edition

Area of window = $\frac{\pi x^2}{4} + x(\frac{30-x-\pi x/2}{2})$ = $f(x)$
As is clear from the diagram, width of the window = diameter of the semicircular part. Let the length of the rectangular portion of the window be $l$. Total perimeter of the window = length of the semicircular arc + length of the rectangle *2 + $x$ = $\pi(x/2) + 2l + x = 30$ So, $l = \frac{30-x-\pi x/2}{2}$ Area of window = area of semicircle + area of rectangle = $\pi (x/2)^2 + xl$ Area of window = $\frac{\pi x^2}{4} + x(\frac{30-x-\pi x/2}{2})$ = $f(x)$