91Ó°ÊÓ

The formula of the area of a rectangle is $A=lw$, where A is the area, l is the length and w is the width of the rectangle.

The formula of the area of a semicircle is $A=\frac{\mathrm{Ï€}{r}^2}{2}$, where A is the area and r is the radius of the semicircle.

The formula of the radius of a semicircle is $r=\frac{d}{2}$, where d is the diameter of the semicircle.

The given figure is a combination of a rectangle and a semicircle.

The length and width of the rectangle are 2.9 cm and 1.2 cm respectively, while the diameter of the semicircle is equal to the width of the rectangle, that is, 1.2 cm.

Then, for the rectangle, $l=2.9\mathrm{cm}$, $w=1.2\mathrm{cm}$and for the semicircle, $d=1.2\mathrm{cm}$.

Put $d=1.2$in $r=\frac{d}{2}$to get,

$$\begin{gathered} r=\frac{1.2}{2} \\ =0.6 \end{gathered}$$

So, $r=0.6$.

Put $l=2.9$and $w=1.2$in $A=lw$to get the area of the rectangle as,

role="math" localid="1642495163759" $$\begin{gathered} A=\left(2.9\right)\left(1.2\right) \\ =3.48 \end{gathered}$$

Put $r=0.6$and $\mathrm{Ï€}=\frac{22}{7}$in $A=\frac{\mathrm{Ï€}{r}^2}{2}$to get the area of the semicircle as,

$$\begin{gathered} A=\frac{\frac{22}{7}{\left(0.6\right)}^2}{2} \\ =\frac{\frac{22}{7}\left(0.36\right)}{2} \\ =\frac{11}{7}\left(0.36\right) \\ ≈0.5657\left(\mathrm{roundedto}4\mathrm{decimalplaces}\right) \end{gathered}$$

Then, the total area of the figure is $3.48+0.5657=4.0457$, that is, approximately 4.0457.

Since the units of length and width of the rectangle and the diameter of the semicircle are all given as centimeters, the unit of their area and thus the unit of the total area of the figure must be square centimeters.

So, the area of the given figure is approximately 4.0457 square centimeters. Rounding to the nearest tenth, the area is 4.0 square centimeters.