Respuesta :
We have a square with two half circles drawn, and we need to find the area of the yellow region.
The procedure we will follow is: first calculate the area of the square, then subtract the area of the two half circles (which make up 1 circle) and then divide the result by 2.
Step 1. Find the area of the square.
The formula to find the area of a square is:
[tex]A_{\text{square}}=l^2[/tex]Where l is the length of the side of the square
[tex]l=6in[/tex]Thus, the area of the square is:
[tex]\begin{gathered} A_{\text{square}}=(6in)^2 \\ A_{\text{square}}=36in^2 \end{gathered}[/tex]Step 2. Calculate the area of the two half circles.
Between the two half circles drawn, we can form one whole circle.
The formula to find the area of a circle is:
[tex]A_{\text{circle}}=\pi r^2[/tex]Where r is the radius of the circle and π=3.1416.
The radius of the circle of half of the side of the square:
[tex]\begin{gathered} r=\frac{6in}{2} \\ r=3in \end{gathered}[/tex]Thus, the area of the circle is:
[tex]\begin{gathered} A_{\text{circle}}=(3.1416)(3in)^2 \\ A_{\text{circle}}=(3.1416)(9in^2) \\ A_{\text{circle}}=28.2744in^2 \end{gathered}[/tex]Step 3. The yellow area will be the result of subtracting the area of the circle to the area of the square and dividing the result by 2:
[tex]A_{\text{yellow}}=\frac{A_{\text{square}}-A_{\text{circle}}}{2}[/tex]Substituting the known values:
[tex]A_{\text{yellow}}=\frac{36in^2-28.2744in^2}{2}[/tex]Solving the operations:
[tex]\begin{gathered} A_{\text{yellow}}=\frac{7.7256in^2}{2} \\ A_{\text{yellow}}=3.863in^2 \end{gathered}[/tex]Finally, we round the answer to the nearest tenth:
[tex]A_{\text{yellow}}=3.9in^2[/tex]Answer:
[tex]3.9in^2[/tex]