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Sagot :
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
[tex]Area=a^2[/tex]
Where, a is the side length of the square.
Putting a=22, we get
[tex]A_1=(22)^2[/tex]
[tex]A_1=484[/tex]
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:
[tex]Area=\dfrac{1}{2}\pi r^2[/tex]
Where, r is the radius of the semicircle.
Putting r=11 and [tex]\pi=3.14[/tex], we get
[tex]A_2=\dfrac{1}{2}(3.14)(11)^2[/tex]
[tex]A_2=1.57(121)[/tex]
[tex]A_2=189.97[/tex]
So, the area of the semicircle is 189.97 sq. inches.
Now, the total area of the banner is
[tex]A=A_1+A_2[/tex]
[tex]A=484+189.97[/tex]
[tex]A=673.97[/tex]
Therefore, the total area of the banner is 673.97 sq. inches.
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