Respuesta :
First, we are going to calculate the area of the semicircle.
The area of a circle is given by the following expression:
[tex]\begin{gathered} A=\frac{\pi}{4}\text{ }\times D^2 \\ D=\text{ diameter} \\ A=\frac{\pi}{4}\text{ }\times(8)^2 \\ A=50.26 \end{gathered}[/tex]As in the figure we have a semicircle, we have to divide the value of the Area by 2,
[tex]\begin{gathered} \text{Area of the Semicircle= }\frac{50.26}{2} \\ \text{Area of the Semicircle= }25.13m^2 \end{gathered}[/tex]Now we have to calculate the area of the trapezoid,
[tex]\begin{gathered} A=\frac{a+b}{2}\times h \\ a=\text{ minor base} \\ b=\text{ major base} \\ h=\text{ height} \end{gathered}[/tex][tex]\begin{gathered} A=\frac{8+12}{2}\times4 \\ A=40m^2 \end{gathered}[/tex]Now we add both values, area of the semicircle and area of the trapezoid,
[tex]\begin{gathered} \text{Area semicircle + Area trapezoid = 25.13+40 } \\ \text{Area semicircle + Area trapezoid = 65.13} \end{gathered}[/tex]Answer= 65.13 square meters
