Answer:
![(a)\ Area = 3765.32](https://tex.z-dn.net/?f=%28a%29%5C%20Area%20%3D%203765.32)
![(b)\ Area = 4773](https://tex.z-dn.net/?f=%28b%29%5C%20Area%20%3D%204773)
Step-by-step explanation:
Given
--- area of each square
![Shade = 4in](https://tex.z-dn.net/?f=Shade%20%3D%204in)
See attachment for window
Solving (a): Area of the window
First, we calculate the dimension of each square
Let the length be L;
So:
![L^2 = A_1](https://tex.z-dn.net/?f=L%5E2%20%3D%20A_1)
![L^2 = 169](https://tex.z-dn.net/?f=L%5E2%20%3D%20169)
![L = \sqrt{169](https://tex.z-dn.net/?f=L%20%3D%20%5Csqrt%7B169)
![L=13](https://tex.z-dn.net/?f=L%3D13)
The length of two squares make up the radius of the semicircle.
So:
![r = 2 * L](https://tex.z-dn.net/?f=r%20%3D%202%20%2A%20L)
![r = 2*13](https://tex.z-dn.net/?f=r%20%3D%202%2A13)
![r = 26](https://tex.z-dn.net/?f=r%20%3D%2026)
The window is made up of a larger square and a semi-circle
Next, calculate the area of the larger square.
16 small squares made up the larger square.
So, the area is:
![A_2 = 16 * 169](https://tex.z-dn.net/?f=A_2%20%3D%2016%20%2A%20169)
![A_2 = 2704](https://tex.z-dn.net/?f=A_2%20%3D%202704)
The area of the semicircle is:
![A_3 = \frac{\pi r^2}{2}](https://tex.z-dn.net/?f=A_3%20%3D%20%5Cfrac%7B%5Cpi%20r%5E2%7D%7B2%7D)
![A_3 = \frac{3.14 * 26^2}{2}](https://tex.z-dn.net/?f=A_3%20%3D%20%5Cfrac%7B3.14%20%2A%2026%5E2%7D%7B2%7D)
![A_3 = 1061.32](https://tex.z-dn.net/?f=A_3%20%3D%201061.32)
So, the area of the window is:
![Area = A_2 + A_3](https://tex.z-dn.net/?f=Area%20%3D%20A_2%20%2B%20A_3)
![Area = 2704 + 1061.32](https://tex.z-dn.net/?f=Area%20%3D%202704%20%2B%201061.32)
![Area = 3765.32](https://tex.z-dn.net/?f=Area%20%3D%203765.32)
Solving (b): Area of the shade
The shade extends 4 inches beyond the window.
This means that;
The bottom length is now; Initial length + 8
And the height is: Initial height + 4
In (a), the length of each square is calculated as: 13in
4 squares make up the length and the height.
So, the new dimension is:
![Length = 4 * 13 + 8](https://tex.z-dn.net/?f=Length%20%3D%204%20%2A%2013%20%2B%208)
![Length = 60](https://tex.z-dn.net/?f=Length%20%3D%2060)
![Height = 4*13 + 4](https://tex.z-dn.net/?f=Height%20%3D%204%2A13%20%2B%204)
![Height = 56](https://tex.z-dn.net/?f=Height%20%3D%2056)
The area is:
![A_1 = 60 * 56 = 3360](https://tex.z-dn.net/?f=A_1%20%3D%2060%20%2A%2056%20%3D%203360)
The radius of the semicircle becomes initial radius + 4
![r = 26 + 4 = 30](https://tex.z-dn.net/?f=r%20%3D%2026%20%2B%204%20%3D%2030)
The area is:
![A_2 = \frac{3.14 * 30^2}{2} = 1413](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B3.14%20%2A%2030%5E2%7D%7B2%7D%20%3D%201413)
The area of the shade is:
![Area = A_1 + A_2](https://tex.z-dn.net/?f=Area%20%3D%20A_1%20%2B%20A_2)
![Area = 3360 + 1413](https://tex.z-dn.net/?f=Area%20%3D%203360%20%2B%201413)
![Area = 4773](https://tex.z-dn.net/?f=Area%20%3D%204773)