Question

In the figure, assume that angles that appear to be right angles are right angles

Answer 1

Answer: $71.13\ units^2$

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:

$A_{sc}=\frac{\pi r^2}{2}$

Where "r" is the radius.

In this case you can see that:

$r=3$

Therefore, its area is (Using 3.14 for $\pi$):

$A_{sc}=\frac{(3.14)( 3\ units)^2}{2}=14.13\ \ units^2$

2.The area of the trapezoid can be found with:

$A_t=\frac{h(B+b)}{2}$

Where "h" is the height and "B" and "b" are the lenghts of the bases.

In this case:

$h=6\ units\\\\B=11\ units\\\\b=8\ units$

Then. its area is:

$A_t=\frac{(6)(11+8)}{2}=57\ units^2$

3. Adding those areas, you get that the area of the figure is:

$A_f=14.13 \ units^2+57\ units^2=71.13\ units^2$