In order to find the area of the semicircle, or the shaded region, we just have to find the area of the entire circle and divide it by 2. The formula for the area of a circle is
![\pi r^(2)](https://img.qammunity.org/2019/formulas/mathematics/college/sw1e9itehmwx8x9b6mwg4ksc0bqhzf7oqa.png)
. With the given diameter of 12, we can deduce that the radius is 6.
Area of Semicircle = (
![\pi 6^(2)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/tgj7h2xf452hyh1n5cnycmt8dse72m4ciq.png)
/2)
Area of Semicircle = (3.14 x 36/2)
Area of Semicircle = (3.14 x 18)
Area of Semicircle = 56.52
![in.^(2)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/b696c7lnyzqf8mhbiigqs4e3dj03a2dhl5.png)
Hope this helps!