Answer:
B. 37 cm²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where $s$ is the side length.\\\end{minipage}}[/tex]
Given the side length of the square is 4 cm:
[tex]\begin{aligned}\implies \sf Area\;of\;the\;square&=4^2\\&=\sf 16\;cm^2\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where $r$ is the radius. \\\end{minipage}}[/tex]
The radius of a circle is half its diameter.
Given the diameter of the semicircles is 2 cm, then their radius is 1 cm.
[tex]\begin{aligned}\implies \textsf{Area of one semicircle}&= \sf \dfrac{1}{2} \pi (1)^2\\& = \sf \dfrac{1}{2} \pi \; cm^2\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a trapezoid}\\\\$A=\dfrac{1}{2}(a+b)h$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the bases. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given the bases of the trapezoids are 2 cm and 4 cm, and their height is 3 cm:
[tex]\begin{aligned}\implies \textsf{Area of one trapezoid}&= \sf \dfrac{1}{2} (2+4)(3)\\&= \sf \dfrac{1}{2} (6)(3)\\&= \sf (3)(3)\\&=\sf 9\;cm^2\end{aligned}[/tex]
Given the figure is made up of a square, two congruent trapezoids and two congruent semicircles:
[tex]\begin{aligned}\implies\textsf{Area of the figure}&= \sf square+2\;trapezoids+2\; semicircles\\&= \sf 16+2(9)+2\left(\dfrac{1}{2} \pi\right)\\& = \sf 16 + 18 + \pi \\& = \sf 34 + \pi \\& = \sf 37.14159...\; cm^2\end{aligned}[/tex]
Therefore, the measurement that is closest to the area of the figure in square centimeters is 37 cm².
