Given:
A banner is made of a square and a semicircle.
Side lengths of the square = 22 inches
Diameter of semicircle is equal to the side length of square.
To find:
The total area of the banner.
Solution:
We know that, the area of a square is
![Area=a^2](https://tex.z-dn.net/?f=Area%3Da%5E2)
Where, a is the side length of the square.
Putting a=22, we get
![A_1=(22)^2](https://tex.z-dn.net/?f=A_1%3D%2822%29%5E2)
![A_1=484](https://tex.z-dn.net/?f=A_1%3D484)
So, the area of the square is 484 sq. inches.
Diameter of semicircle = Side length of square = 22 inches
Radius of semicircle = 11 inches.
The area of a semicircle is:
![Area=\dfrac{1}{2}\pi r^2](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Cpi%20r%5E2)
Where, r is the radius of the semicircle.
Putting r=11 and
, we get
![A_2=\dfrac{1}{2}(3.14)(11)^2](https://tex.z-dn.net/?f=A_2%3D%5Cdfrac%7B1%7D%7B2%7D%283.14%29%2811%29%5E2)
![A_2=1.57(121)](https://tex.z-dn.net/?f=A_2%3D1.57%28121%29)
![A_2=189.97](https://tex.z-dn.net/?f=A_2%3D189.97)
So, the area of the semicircle is 189.97 sq. inches.
Now, the total area of the banner is
![A=A_1+A_2](https://tex.z-dn.net/?f=A%3DA_1%2BA_2)
![A=484+189.97](https://tex.z-dn.net/?f=A%3D484%2B189.97)
![A=673.97](https://tex.z-dn.net/?f=A%3D673.97)
Therefore, the total area of the banner is 673.97 sq. inches.