Explanation:
First we have to find the areas of each piece and then add them up.
The area of a triangle is the length of the base multiplied by its height and divided by 2:
[tex]A_{\text{triangle}}=\frac{12in\times6in}{2}=36in^2[/tex]
The area of a rectangle is the product of the lengths of the sides:
[tex]A_{\text{rectangle}}=10in\times12in=120in^2[/tex]
The area of a circle is pi times the radius squared. For a semicircle it's half the area of the circle:
[tex]A_{\text{semicircle}}=\frac{\pi r^2}{2}=\frac{\pi\cdot5^2}{2}=\frac{25}{2}\pi\approx40in^2[/tex]
The total area of the flag is:
[tex]\begin{gathered} A=A_{\text{triangle}}+A_{\text{rectangle}}+A_{\text{semicircle}} \\ A=36in^2+120in^2+40in^2 \\ A=196in^2 \end{gathered}[/tex]
Answer:
B. 196 in²
