SOLUTION: I just cannot figure this out. Please help me: a sign is in the shape of a square with a semicircle of a radius x adjoining one side and a semicircle of diameter x removed from th

Algebra ->  Functions -> SOLUTION: I just cannot figure this out. Please help me: a sign is in the shape of a square with a semicircle of a radius x adjoining one side and a semicircle of diameter x removed from th      Log On


   

Question 241467: I just cannot figure this out. Please help me: a sign is in the shape of a square with a semicircle of a radius x adjoining one side and a semicircle of diameter x removed from the opposite side. If the side of the square are length 2x, then write the area of the sign as a function of x.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think it looks like this:
___
)___ )

The area of the semi-circle added to one side
is %281%2F2%29%2Api%2Ax%5E2
The area of the square is 2x%2A2x+=+4x%5E2
So far the area of the sign is
4x%5E2+%2B+%281%2F2%29%2Api%2Ax%5E2
The semi-circle that is removed
has radius = x%2F2
It's area is %281%2F2%29%2Api%2A%28x%2F2%29%5E2
So, the area of the sign is
4x%5E2+%2B+%281%2F2%29%2Api%2Ax%5E2+-+%281%2F2%29%2Api%2A%28x%2F2%29%5E2
4x%5E2+%2B+%281%2F2%29%2Api%2Ax%5E2+-+%281%2F2%29%2Api%2A%28x%5E2%2F4%29
Factor out x%5E2
x%5E2%2A%284+%2B+%281%2F2%29%2Api+-+%281%2F8%29%2Api%29
Factor out pi
x%5E2%2A%284+%2B+%281%2F2+-+1%2F8%29%2Api%29
x%5E2%2A%284+%2B+%283%2F8%29%2Api%29
Hope I got it