Answer:
41.1 units²
Step-by-step explanation:
The given figure is composed of a semicircle and a triangle.
The diameter of the circle = the base of the triangle = the distance between point D and point F on the x-axis.
Therefore,
Diameter (d) of circle = 8 units
Radius of circle = [tex] \frac{diameter}{2} = \frac{8}{2} [/tex]
[tex] radius (r) = 2 [/tex]
Base of triangle = 8 units
The height of the triangle = the perpendicular distance between point E and segment DF on the y-axis
Height of triangle = 4 units
=>Area of the figure = area of triangle + area of semicircle
Area of figure = [tex] \frac{1}{2}bh + \frac{1}{2}*pie*r^2[/tex]
[tex] = \frac{1}{2}*8*4 + \frac{1}{2}*3.14*4^2[/tex]
[tex] = \frac{1}{2}*32 + \frac{1}{2}*50.24[/tex]
[tex] = 16 + 25.12 [/tex]
[tex] = 41.12 [/tex]
Area of the figure = 41.1 units² (to the nearest tenth)
