Question 918440
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A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 36.900 ft. give
the area A of the window in square feet when the width is 7.500 ft. Give the answer to two decimal places.
I'm stuck and I need this one to finish my homework! Even my dad can't help me and I got no results from google and my math
book only uses rectangular examples!!! PLEASE HELP ME!!!!
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Respondent @josgaritmetic presumes that additional info is needed to determine the area in this problem. Quite the contrary!   
  *[illustration ADC_918440_4.png].
This problem was redone and corrected, since the width and perimeter were erroneously entered before as 7,500 and 36,900,
respectively, instead of 7.5' and 36.9', respectively 

      Width (W), or DC = 7.5’
Diameter of semi-circle = AB = DC = W = 7.5'
   Perimeter (GIVEN) = 36.9’
Perimeter of window = BCDA + length of arc of semi-circle AB 
                                     = L + W + L + circumference of semicircle (length of arc AB) 
                                     = W + 2L + circumference of semicircle (length of arc AB)
                             36.9 = 7.5 + 2L + {{{(1/2)}}}ꙥD ---- Substituting 36.9 for perimeter, 7.5 for W, and {{{(1/2)}}}ꙥD for circumference of
                                                                                  semi-circle, AB
                             36.9 = 7.5 + 2L + {{{(1/2)}}}ꙥAB
                             36.9 = 7.5 + 2L + {{{(1/2)}}}7.5ꙥ
                             36.9 = 7.5 + 2L + 3.75ꙥ
       36.9 - 7.5 - 3.75ꙥ = 2L
                29.4 - 3.75ꙥ = 2L
           {{{(29.4 - 3.75pi)/2 = L}}}
                             8.81' = L              
Area of rectangle, ABCD: LW = 8.81(7.5) = 66.075 sq ft


Diameter of semi-circle, AB = AB
Radius (r) = {{{1/2}}}D = {{{1/2}}}AB = {{{1/2}}}7.5 = 3.75’
Area of semi-circle AB = {{{(1/2)pi*r^2}}} 
                                      = {{{(1/2)3.75^2}}}ꙥ ---- Substituting 3.75 for r 
                                      = {{{1/2}}}(14.0625ꙥ) 
                                      = {{{1/2}}}(44.17864) = 22.08932 sq ft

<font color = red><font size = 3>Area of the window</font></font> = Area of rectangle, ABCD + Area of semi-circle AB 
                                          =             66.075 sq ft         +        22.08932 sq ft = 88.16432, or <font color = red><font size = 3>approximately 88.16 sq ft <font color = red><font size = 3></font></font></font></font></font></b></pre>