Answer:
[tex]23.42 \, \textsf{cm}[/tex]
Step-by-step explanation:
To find the perimeter of the figure, we need to add the lengths of all the sides.
The rectangle has sides of length 4 cm and 6 cm.
Here, we need to add three sides only:
So, sum of the three sides of the rectangle is:
[tex]4 \, \textsf{cm} + 6 \, \textsf{cm} + 4 \, \textsf{cm} = 14 \, \textsf{cm}[/tex].
Now, for the semicircle, we only need to consider its curved part. The formula for the circumference of a full circle is:
[tex]2\pi r[/tex]
For a semicircle, we take half of this circumference, so it becomes [tex]\pi r[/tex].
Given that the radius [tex]r[/tex] of the semicircle is 3 cm, we can calculate the curved part's perimeter as:
[tex] \pi \times 3 \, \textsf{cm} = 3.14 \times 3 \, \textsf{cm} = 9.42 \, \textsf{cm}[/tex]
Now, adding the perimeter of the rectangle (3 sides) and the curved part of the semicircle, we get:
[tex]\textsf{Perimeter} = 14 \, \textsf{cm} + 9.42 \, \textsf{cm} [/tex]
[tex]\textsf{Perimeter} = 23.42 \, \textsf{cm}[/tex]
So, the perimeter of the figure is [tex]23.42 \, \textsf{cm}[/tex].
