Answer:
28.095 cm^2
Explanation:
To determine the area of the given shape, we have to determine the area of the complete rectangle, then subtract the areas of each of the cut-out semi-circles as seen below;
From the shape, let's determine the length and width of the rectangle;
Length(l) = 2 cm + 5 cm + 2 cm = 9 cm
Width(w) = 1 cm + 4 cm + 1 cm = 6 cm
So the area of the complete rectangle will be;
[tex]\begin{gathered} A_r=l\cdot w=9\cdot6=54cm^2 \\ \text{where;} \\ A_r=\text{ Area of the complete rectangle} \end{gathered}[/tex]
Let's now determine the area of the top semi-circle given that the radius is 2cm (radius = diameter/2 = 4/2 = 2cm);
[tex]\begin{gathered} A_{\text{tsc}}=\frac{\pi r^2}{2}=\frac{3.14(2)^2}{2}=\frac{3.14\cdot4}{2}=\frac{12.56}{2}=6.28cm^2 \\ \text{where;} \\ A_{\text{tsc}}=\text{Area of top semi-circle} \end{gathered}[/tex]
Given that the two semi-circles by the side of the rectangle have the same radius(r) which is 2.5cm (r = diameter/2 = 5/2 = 2.5cm), let's go ahead and determine their area;
[tex]\begin{gathered} A_{\text{ssc}}=2(\frac{\pi r^2}{2})=\pi r^2=3.14\cdot(2.5)^2=3.14\cdot6.25=19.625cm^2 \\ \text{where;} \\ A_{\text{ssc}}=\text{Area of side semi-circles} \end{gathered}[/tex]
So the area of the shape will be;
[tex]\begin{gathered} A=A_r-A_{\text{tsc}}-A_{\text{ssc}}=54-6.28-19.625=28.095cm^2 \\ \end{gathered}[/tex]
Therefore, the area of the shape is 28.095 cm^2
