Help with Functions: Find the Area of a Norman Window

[thegame1234]

Help with Functions!

Hi everone this is my first thread and I am looking forward to particitate in PF. Anyways I need help with a question...although I found a solution but I am not sure if it is right..any help would be greatly appreaciated.
Question - A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30ft, express the area A of the window as a function of the width x of the window.
Solution - 2x+2y=30, solvin for y; y=15/2-x
A=Rectangle + semicircle
A=xy + "pi"(x/2)^2
A=x(15/2-x)+"pi"x^2/4
A=15x/2-x^2+"pi"x^2/4
Well...it looks pretty simple but last assignment I did, I got a low mark and I screwed up in many places...so I just want to make sure it doesn't happen again...thanks in advance.

 

[quasar987]

Hi the game, warm welcome to PF ! You have found homework help paradise.

I'm afraid I disagree with your first equation .

You give 2x+2y=30 as the equation of the perimeter. But this looks to me like the equation for the perimeter of a rectangular window! Try working out a new perimeter equation considering the circular higher part of the window.

And keep in mind when you use the equation of perimeter and area of a circle that you are dealing with a semicircle. Hence you must divide these expressions by half! Ex: the equation of the area and perimeter of the semi-circle are respectively

$$A = \frac{1}{2}\pi r^2$$

$$P = \pi r$$

 

[thegame1234]

Thanks quasar987...I really appreaciate your help...I love PF homework help :)