First, we will establish that the shape of the window is a semi-circle. This means we must use the formula for the perimeter of a semi-circle to obtain the perimeter of the window.
The formula for the perimeter of a semi-circle is as follows:
Let perimeter of window or semi-circle = P
P = [ 2( Pi )r / 2 ] + 2r
Where r = radius of circle or semi-circle
From this, we will simply use the value of the radius given from the diagram in the problem and substitute it into the formula to obtain the perimeter of the window.
P = [ 2( Pi )r / 2 ] + 2r
r = 20
THEREFORE:
P = [ 2( Pi )( 20 ) / 2 ] + 2( 20 )
P = 20( Pi ) + 40
P = 102.83...cm^2
P = 102.8cm^2 ( to the nearest tenth )
FINAL ANSWER:
Therefore, the perimeter of the window is 102.8cm^2 ( to the nearest tenth ).
