the area of the shaded region is 14.43 square units
Explanation
to solve this we need to subtrac the area of a half circle from the area of the rectangle, so
Step 1
find the areas
a) rectangle
the area of a rectangle is given by:
note that thewidth of the rectangle equals the diameter of the circle, so
[tex]\begin{gathered} Area=2\text{ *8= 16 square units} \\ Area_{rectangle}=16\text{ \lparen un}^2) \end{gathered}[/tex]
b)half circle
the area of half circle is given by:
[tex]Area_{halfcircle}=\pi(\frac{diamter^2}{8})[/tex]
so, let
diameter = 2
and replace
[tex]\begin{gathered} Area_{halfcircle}=3.14(\frac{2^2}{8}) \\ Area_{halfcircle}=3.14*\frac{1}{2}=1.57 \\ Area_{halfcircle}=1.57\text{ \lparen un}^2) \end{gathered}[/tex]
Step 3
finally, subtract the areas, so
[tex]16.-1.57=14.43[/tex]
so, the area of the shaded region is 14.43 square units
I hope this helps you
