A Norman window has the shape of a square with a semicircle mounted on it. What is the width of the window if the total area of the square and the semicircle is to be 200 ft^2?

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Answer 1 · 2017-09-16T08:24:20

Width of window is #11.984# #ft.#

Let the width of window be #xft#.

Then the diameter of semicircle too is #xft#.

Hence area of window is #x^2+pi/2xx(x/2)^2#

i.e. #x^2xx(1+pi/8)#

As such #(1+pi/8)x^2=200#

and #x=sqrt(200/(1+pi/8))#

#=10xxsqrt(2/(1+pi/8))=10xxsqrt(16/(8+pi))#

#=10xxsqrt(16/11.14159)=1.1984xx10=11.984#

Hence, width of window is #11.984# #ft.#