In the given figure there is a rectangle, and the semi circle at one side of the rectangle so, the diameter of the circle is equal to the length of the rectangle:
SInce semi circle is inscribed in the rectangel so,
[tex]\text{Perimeter of Shaded region=Perimeter of Rectangle without one side+Perimeter of Semicircle}[/tex]In the given figure the Length of the rectangle : 6m
Breadth of rectangle : 8m
Expression for the perimeter of rectangle is:
[tex]\begin{gathered} \text{ Perimeter of Rectangle = 2}\times(Length+breadth) \\ \text{Substitute the value of length and breadth from the given data} \\ \text{Perimeter of given rectangle = 2(6+8)} \\ \text{Perimeter of given rectangle = 28m} \end{gathered}[/tex]Perimeter of the circle is aslo known as the circumference of the circle So
The expression for the Circumference of the circle is :
[tex]\begin{gathered} \text{ Circumference of Circle =2 }\times\Pi\times\text{ Radius} \\ \text{ Since, Semicircle is the half of the circle} \\ S\text{o, the circumference of the semicircle is the half of the circumference of the circle} \\ \text{Circumference of the semi circle=}\frac{\text{2 }\times\Pi\times\text{ Radius}}{2} \\ \text{Circumference of the semicircle=}\Pi\times\text{ Radius} \\ \text{ From the given figure the Diameter of the semi circle is the length of the rectangle SO,} \\ \text{Diamter of semicircle=6m} \\ \text{Radius is the half of the diameter} \\ So,\text{ Radius of Semicircle =}\frac{6}{2}m \\ \text{Radius of Semicircle =3m} \\ \text{Substitute the value of radius in the expression of circumference} \\ \text{Circumfrence of Given semicircle is : }\Pi\times3m \\ \text{ SInce }\Pi=3.14 \\ \text{Circumference of the given semicircle = 9.42m} \end{gathered}[/tex]Now, for the perimeter of the shaded region
The perimeter of the shaded region
In the given figure of shaded region we have , 2 breadth of 8m each , one length of 6m and the circumference of the semicircle
So, the perimeter will be :
[tex]\begin{gathered} \text{Perimeter of Shaded region = Measurement of Length + 2}\times Measurement\text{ of Breadth+Circumference of Semicircle} \\ Perimeter\text{ of the shaded region = 6+2}\times8+9.42 \\ \text{ Perimeter of the shaded region=31.42m} \end{gathered}[/tex]Answer :
Perimeter of the shaded region is 31.42 m
