Step-by-step explanation:
Given
A semi-circle is placed over a rectangle
width of the rectangle is w=1.5 cm
The length of the rectangle is l=9.2 cm
from the figure, we can write
[tex]\Rightarrow 9.2=2.5+2r\quad (\text{length of rectangle is equal})[/tex]
where r=radius of the semi-circle
[tex]\Rightarrow 2r=6.7\\\Rightarrow r=3.35\ cm[/tex]
Perimeter of figure
[tex]\Rightarrow 9.2+1.5+2.5+\pi r+1.5\\\Rightarrow 14.7+10.52=25.22\ cm[/tex]
Area of the figure
[tex]\Rightarrow A=\text{Area of rectangle+Area of semi-circle}\\\Rightarrow A=1.5\times 9.2+\pi \times 3.35^2\\\Rightarrow A=13.8+35.26=49.06\ cm^2[/tex]
