EXPLANATION
Since we have a semicircle and a right triangle, we first need to compute the area of each shape and then add the surfaces:
Area of the right triangle:
[tex]\frac{1}{2}\cdot\text{Base}\cdot\text{Height}=[/tex]
The base is equal to 6ft and the height is equal to 8 ft:
The area of the triangle is as follows:
[tex]=\frac{1}{2}\cdot6\cdot8=24ft^2[/tex]
Now, the area of the semicircle is given by the following equation:
[tex]\text{Area}_{\text{semicircle}}=3.14\cdot\frac{r^2}{2}[/tex]
Where r= radius = diameter/2 = 8/2 = 4
Plugging in the values:
[tex]Area_{semicircle}=3.14\cdot\frac{4^2}{2}=3.14\cdot\frac{16}{2}=3.14\cdot8=25.12ft^2[/tex]
Finally, we need to add the surfaces:
Area=Area_right triangle + Area_semicircle
Area = 24+25.12 = 49.12 ft^2
In conclusion, the solution is 49.12 ft^2
