Perimeter of the shape [tex]$=18\pi[/tex] cm
Area of the shape [tex]$=108\pi[/tex] cm²
Solution:
Diameter of the semi-circle AB = BC = CD = 6 cm
Radius of AB = BC = CD = 6 ÷ 2 = 3 cm
Diameter of the semi-circle AD = 6 + 6 + 6 = 18 cm
Radius of the semi-circle AD = 18 ÷ 2 = 9 cm
Let us first find the perimeter of the shape:
Perimeter of the semi-circle AB = [tex]\pi r[/tex]
[tex]$=\pi\times3[/tex]
Perimeter of the semi-circle AB [tex]$=3\pi[/tex] cm
Perimeter of the semi-circle AD = [tex]\pi r[/tex]
[tex]$=\pi\times9[/tex]
Perimeter of the semi-circle AD [tex]$=9\pi[/tex] cm
Perimeter of the shape = Perimeter of (AB + BC + CD) + Perimeter of AD
[tex]$=3\pi+3\pi+3\pi+9\pi[/tex]
[tex]$=18\pi[/tex] cm
Perimeter of the shape [tex]$=18\pi[/tex] cm
To find the area of the shape:
Area of the semi-circle AB = [tex]\pi r^2[/tex]
[tex]=\pi\times 3^2[/tex]
Area of the semi-circle AB [tex]=9\pi[/tex] cm²
Area of the semi-circle AD = [tex]\pi r^2[/tex]
[tex]=\pi\times 9^2[/tex]
Area of the semi-circle AD [tex]=81\pi[/tex] cm²
Area of the shape = Area of (AB + BC + CD) + Area of AD
[tex]$=9\pi+9\pi+9\pi+81\pi[/tex]
[tex]$=108\pi[/tex] cm²
Area of the shape [tex]$=108\pi[/tex] cm²
Perimeter of the shape [tex]$=18\pi[/tex] cm
Area of the shape [tex]$=108\pi[/tex] cm²
