The area of the shaded region is 164.52 inches squared
Here, we wan to calculate the area of the shape given
From what we have, there is a triangle and a semi-circle
So the area of the shape is the sum of the areas of the triangle and the semi-circle
Mathematically, we can have this as;
[tex]\begin{gathered} \text{Area of triangle = }\frac{1}{2}\text{ }\times\text{ b }\times\text{ h} \\ \\ \text{Area of semicircle = }\frac{\pi\text{ }\times r^2}{2} \end{gathered}[/tex]where b represents the base of the triangle which is the diameter of the semicircle
The radius of the semicircle is 6 inches and the diameter is 2 times of this which equals 2 * 6 = 12 inches
The height of the triangle is 18 inches
The radius of the semicircle is 6 inches as above
Thus, we have the area of the shape as follows;
[tex]\begin{gathered} (\frac{1}{2}\times\text{ 18 }\times\text{ 12) + (}\frac{3.14\text{ }\times6^2}{2}) \\ \\ =\text{ 108 + 56.52} \\ \\ =\text{ 164.52 inches squared} \end{gathered}[/tex]