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A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the window with a perimeter of 45 feet?
Wiki User
∙ 16y ago
The area is 2*h*(45-2*h)/(2+pi) where h is the height of the rectangular part of the door.
Wiki User
∙ 9y ago
Dania Dereje
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A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 45 feet?
To solve this problem, let's break it down step by step. Let ( r ) be the radius of the semicircle, which is also the width of the rectangle. The perimeter of this figure (Norman window) is given as 45 feet: The perimeter, ( P ), is the sum of the parts: the semicircle's circumference and the perimeter of the rectangle. The semicircle's circumference: ( \pi r ) The perimeter of the rectangle: ( 2r + 2r = 4r ) So, the total perimeter equation is: [ \pi r + 4r = 45 ] This simplifies to: [ \pi r + 4r = 45 ] [ (\pi + 4) r = 45 ] [ r = \frac{45}{\pi + 4} ] Now, we need to find the total area of the figure. The area of the semicircle is: [ \frac{\pi r^2}{2} ] The area of the rectangle is: [ r \times 2r = 2r^2 ] The total area, ( A ), is the sum of these two parts: [ A = \frac{\pi r^2}{2} + 2r^2 ] Substitute the value of ( r ) derived earlier: [ A = \frac{\pi (\frac{45}{\pi + 4})^2}{2} + 2(\frac{45}{\pi + 4})^2 ] Calculating this would give the area of the largest possible Norman window with a perimeter of 45 feet.
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle What is the area of the largest possibe Norman window with?
These windows could get extremely large, but let's play with Andersen Windows' catalog. If you build a Norman window using Andersen's largest semicircle window, which is six feet wide, and their tallest twin double-hung window, which is 6'4" high, you get an area of 52.11 square feet.
What are the dimensions of a rectangle that can contain a Norman window that measures 15.5 feet?
A Norman window is a semicircle on top of a rectangle. You have given one dimension of 15.5 ft. There is no indication as to which dimension this refers. If it is the width of the window, then the semi-circular bit at the top has a radius of 7.75 ft and there is no indication of the height of the rectangular bit; thus a rectangle that can contain the window is at least 15.5 ft wide and at least 7.75 ft high. If 15.5 ft is the height of the window, then the window can have any width greater than 0 ft and less than 31 ft - the greater the width the shorter the rectangular bit of the window. which means the rectangle will have varying dimensions between a width greater than 0 ft and a height greater than 15.5 ft, to a width of 31 ft and a height greater than 15.5 ft; in this case a rectangle greater than 31 ft by greater than 15.5 ft will contain any possible Norman window that is 15.5 ft high. (At 31ft by 15.5 ft the rectangle will cover the widest Norman window possible.)
A window consists of an open rectangle topped by a semicircle and is to have a perimeter of 288in. find the radius of the semicircle that will maximize the area of the window?
Let x be the width and y be the length of the rectangle. x/2 is the radius of the semicircle Perimeter of the Norman window is x+2y+(π x)/2 Let P be the perimeter --- 288 in this problem. P = x+2y+(π x)/2--------(1) Solving for y from equation (1) 2y = P-x-πx/2 y = P/2-x/2-πx/4--------(2) Area = xy + π x^2 / 8 A = x(P/2-x/2-π x/4) + π x^2/8 A= Px/2-x^2 /2 -πx^2/4 +πx^2/8 dA/dx = P/2 -2x/2-2πx /4 +2πx / 8 =0 (4p-8x-2πx)/8=0 4p-2x(π+4)=0 4p=2x(π+4) x= 2P / (4+π) The radius is x/2 = P/(4+PI) Substitute P with 288 radius = 288 / (4+PI) will maximize the area of the window. d^2A/dx^2 =-1-π/2+π/4 < 0, indicates that the area is maximized. You'll have to simplify x and y if you want them in numeric format.
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An Anglo-Norman is a Norman who settled in England after the Norman Conquest, or a descendant of one.
What is Anglo-Norman?
An Anglo-Norman is a Norman who settled in England after the Norman Conquest, or a descendant of one.
Who is Norman Lear?
Norman Lear's birth name is Norman Milton Lear.
What is the birth name of Norman Fields?
Norman Field's birth name is Field, Norman Randolph.
Was king william a Norman?
Yes. He was a Norman. He was the first Norman King in England.
What has the author Irving Norman written?
Irving Norman has written: 'Irving Norman'
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Norman Taurog went by Uncle Norman.
Where is the Norman Public Library in Norman located?
The address of the Norman Public Library is: 225 N Webster, Norman, 73069 7133
