I need help with a Precalculus problem?

Question

A norman window has the shape of a rectangle surmounted by a semicircle. if the permeter is 30ft. , find a fuction that models the area of the window

Answer 1

let the width and height of the rectangle be w and h
diameter ofthe semicircle will be w
paerimeter of the semicircle=pi*(w/2)
perimeter of the rectangle=2(w+h)
perimeter of the window=2(w+h)+pi(w/2)
2w+2h+pi*w/2=30
w(2+(pi/2))+2h=30
h=30/[w(2+(pi/2))]/2
area=pih^2/8+wh

Answer 2

I'm making a function in in terms of r (the radius of the semicircle).

Because the perimeter of whole circle is 2 pi r, the perimeter of the semicircle would then be pi r

r would equal to half of the width of the rectangular portion of the window, so the width would equal 2r

Solve for the length of the rectangular portion of the window:

30ft = perimeter of semicircle + width + length
30 = pi r + 2r + length
length = 30 - (pi r + 2r)

Now that you know the dimensions, you can solve for the area.

Area of semicircle: (pi r ^2)/ 2
Area of rectange: (30 - pi r - 2r)(2r) = 60r - 2 pi r^2 - 4 r^2
Area of entire window:

A = (pi r ^2)/ 2 + 60r - 2 pi r^2 - 4 r^2

I know that's messy, so if you just want the area with the variables:

A= l x w + (pi r^2)/ 2

but keep in mind that w = 2r...

Hope this helps. Good luck.

Answer 3

false