Answer: [tex]71.13\ units^2[/tex]
Step-by-step explanation:
The area of the figure is the sum of the area of the semi-circle and the area of the trapezoid.
1.The area of the semi-circle can be found with this formula:
[tex]A_{sc}=\frac{\pi r^2}{2}[/tex]
Where "r" is the radius.
In this case you can see that:
[tex]r=3[/tex]
Therefore, its area is (Using 3.14 for [tex]\pi[/tex]):
[tex]A_{sc}=\frac{(3.14)( 3\ units)^2}{2}=14.13\ \ units^2[/tex]
2.The area of the trapezoid can be found with:
[tex]A_t=\frac{h(B+b)}{2}[/tex]
Where "h" is the height and "B" and "b" are the lenghts of the bases.
In this case:
[tex]h=6\ units\\\\B=11\ units\\\\b=8\ units[/tex]
Then. its area is:
[tex]A_t=\frac{(6)(11+8)}{2}=57\ units^2[/tex]
3. Adding those areas, you get that the area of the figure is:
[tex]A_f=14.13 \ units^2+57\ units^2=71.13\ units^2[/tex]
