Question 706825: I posted a problem several days ago, hoping to get some assistance for assignment due on Monday. Need help please.
A window in the shape of a rectangle with a semicircular top, (Norman window), .
The height of the rectangular part is twice the base. If the base is 6 feet, what is the area? I got 86.13 feet squared.
Then: Assume that the same window has a radius of 2 feet.We want the rectangular part of window to have same area as the semicircular top.What should the dimensions of the rectangle be? Please explain.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The area will be the area of the rectangular part, plus the area of the semicircular part.
For the second part:
If the radius is  ft, the diameter, which is also the width of the rectangle, is
 ft.
That would be the base of the downwind.
and if the height of the rectangular part is twice the base, then that height is
 feet= feet.
Then the area of the rectangular part is 
The area of half of a circle with radius  is
  
The total area is
  = approximately .
For the first part, a rectangle 3 feet by 6 feet would have an area of 72 square feet, and a semicircle with a 6 feet diameter (3 feet radius) would have an area of
 =approximately  ,
for a total area of approximately  .
That is what you found, aside from the rounding difference.
(I used a more accurate version of  , but I would get 86.13 too, If I used 3.14 por ).
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