Answer:
[tex]68.28[/tex]
Step-by-step explanation:
We can break this figure up into 2 rectangles, and 1 semi-circle.
Let find the area of top rectangle.
Area of rectangle is length x width.
The length is 9 and the width is 2.
9x2=18
so the top rectangle area is 18.
Now let find the lower rectangle area
The lower rectangle length is 4 and the width is 11.
So the area is 44.
Now let find the area of the semi circle.
We need to find the diameter of the circle.
The circle coincides with the side of the lower rectangle.
Since opposite sides in rectangle are equal, the right side of the rectangle also measures 11.
The top right side of the figure measure 5 while the bottom measure 2 so we set up an equation
[tex]5 + 2 + x = 11[/tex]
[tex]7 + x = 11[/tex]
[tex]x = 4[/tex]
So our diameter of the circle is 4.
Area of semi circle is
[tex] \frac{1}{2} \times (\pi) \times {r}^{2} [/tex]
where r is the radius.
Since the diameter is 4 and radius is half of the diameter, the radius is 2.
Plug 2 in the equation
[tex] \frac{1}{2} \times \pi \times {2}^{2} [/tex]
[tex] \frac{1}{2} \times \pi \times 4[/tex]
[tex]2\pi[/tex]
[tex]6.28[/tex]
Now let add all the areas,
[tex]18 + 44 + 6.28[/tex]
[tex]68.28[/tex]