Given:
The composite figure consists of a square and three semicircles.
Given that the half of the side of the square is 2 cm.
From the figure, the other half of the same side is also equal, then the side of the square is 2 + 2 = 4 cm.
We need to determine the area of the composite figure.
Area of the square:
The area of the square can be determined using the formula,
[tex]A=s^2[/tex]
where s is the side length of the square.
Substituting s =4 ,we get;
[tex]A=4^2[/tex]
[tex]A=16[/tex]
Thus, the area of the square is 16 cm²
Area of the semicircle:
The area of the semicircle can be determined using the formula,
[tex]A=\frac{\pi r^2}{2}[/tex]
The radius of the semicircle is 2 cm.
Substituting r = 2 in the above formula, we get;
[tex]A=\frac{\pi 4}{2}[/tex]
[tex]A=2 \pi[/tex]
Thus, the area of the semicircle is 2π
Area of the composite figure:
The area of the composite figure can be determined by adding the area of the square and the three semicircles.
Thus, we have;
Area = Area of square + (3 × Area of semicircle)
Substituting the values, we have;
[tex]Area = 16 +(3 \times 2 \pi)[/tex]
[tex]Area = 16+6 \pi[/tex]
Thus, the area of the composite figure is [tex](6 \pi +16) \ cm^2[/tex]
Hence, Option b is the correct answer.
