The area of the window is ![\frac{25x}{2} -(1 +\frac{\pi}{2} )\frac{x^2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B25x%7D%7B2%7D%20-%281%20%2B%5Cfrac%7B%5Cpi%7D%7B2%7D%20%29%5Cfrac%7Bx%5E2%7D%7B2%7D)
The shape of the Norman window is described as a rectangle surmounted by a semicircle.
Let 'x' be the width of the window.
Then this width corresponds to the diameter of the semicircle.
That is, radius of the semicircle = x/2
Now given the perimeter of the whole window = 25 ft
This perimeter is equal to the sum of 3 sides of the rectangle and the perimeter of the semicircle.
Perimeter of the semicircle =
, where r is the radius of the semicircle.
Now let 'y' be the length of the window.
Then sum of three sides of the window = 2y + x
So 2y + x +
= 25
Therefore,
Area of the window = Area of the semicircle + Area of the rectangle =
![\frac{\pi x^2}{8} +xy = \frac{\pi x^2}{8} + x( 25 - x - \frac{\pi x}{2} ) / 2\\ = \frac{\pi x^2}{8} + (25x - x^2 - \frac{\pi x^2}{2} ) / 2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20x%5E2%7D%7B8%7D%20%2Bxy%20%3D%20%5Cfrac%7B%5Cpi%20x%5E2%7D%7B8%7D%20%2B%20x%28%2025%20-%20x%20-%20%5Cfrac%7B%5Cpi%20x%7D%7B2%7D%20%29%20%2F%202%5C%5C%20%3D%20%5Cfrac%7B%5Cpi%20x%5E2%7D%7B8%7D%20%2B%20%2825x%20-%20x%5E2%20-%20%5Cfrac%7B%5Cpi%20x%5E2%7D%7B2%7D%20%29%20%2F%202)
So Area of the window = ![\frac{25x}{2} -(1 +\frac{\pi}{2} )\frac{x^2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B25x%7D%7B2%7D%20-%281%20%2B%5Cfrac%7B%5Cpi%7D%7B2%7D%20%29%5Cfrac%7Bx%5E2%7D%7B2%7D)
Learn more about area of circle and rectangle at brainly.com/question/4694841
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Answer:
0.9
Step-by-step explanation:
If the x stands for multiplying then it will equal 7. take 7 divided by 8 and then multiply that by 8 and you get seven. did that help my dear?