Option A:
The area of the figure is 71.13 square units.
Solution:
The figure is splitted into two shapes.
One is semi-circle and the other is trapezoid.
Radius of the semi-circle = 3
Area of the semi-circle = [tex]\frac{1}{2}\pi r^2[/tex]
[tex]$=\frac{1}{2} \times 3.14 \times 3^2[/tex]
Area of the semi-circle = 14.13 square units
Top base of the trapezoid = 8
Bottom base of the trapezoid = 11
Height of the trapezoid = 6
Area of the trapezoid = [tex]\frac{1}{2}\times\text{sum of the parallel sides}\times\text{Height}[/tex]
[tex]$=\frac{1}{2}\times{(8+11)}\times{6}[/tex]
[tex]$=\frac{1}{2}\times{19}\times{6}[/tex]
Area of the trapezoid= 57 square units
Area of the figure = Area of the semi-circle + Area of the trapezoid
= 14.13 square units + 57 square units
= 71.13 square units
The area of the figure is 71.13 square units.
Hence Option A is the correct answer.
